, ,zadani pro "Adamová, Marie " 105005
Vyjdrete jako elementarni funkci integral z
((3*x^3-13*x^2+19*x-8)*x)/((x-2)^2*(x-1)*(x^2-2*x+2))
=d
x ( )- + -3 x3
13 x2
19 x 8
( )-x 2 2
( )-x 1 ( )- +x2
2 x 2
x d+ +
2
( )-x 2 2
1
-x 1
+2 x 1
- +x2
2 x 2
x
- + + +
2
-x 2
( )ln -x 1 ( )ln - +x2
2 x 2 3 ( )arctan -x 1=
:=line "PMMAT2| 99521|Albrechtová, Kristýna|zk|ESF B-HPS NH [sem 6]"
, ,zadani pro "Albrechtová, Kristýna" 99521
Vyjdrete jako elementarni funkci integral z
(4*x^3-16*x^2+24*x-8)/((x-2)^2*(x^2-4*x+8))
=d
4 ( )- + - +4 x2
6 x 2 x3
( )-x 2 2
( )- +x2
4 x 8
x d+ +
2
( )-x 2 2
2
-x 2
+2 x 2
- +x2
4 x 8
x =
- + + +
2
-x 2
2 ( )ln -x 2 ( )ln - +x2
4 x 8 3 arctan -
x
2
1
:=line "PMMAT2|100108|Babák, Jan |zk|ESF M-HPS RRS [sem 6]"
, ,zadani pro "Babák, Jan " 100108
Vyjdrete jako elementarni funkci integral z
(4*x^4-19*x^3+27*x^2-7*x-9)/((x-1)^2*(x-3)*(x^2-4*x+5))
=d
- + - -4 x4
19 x3
27 x2
7 x 9
( )-x 1 2
( )-x 3 ( )- +x2
4 x 5
x d+ +
1
( )-x 1 2
3
-x 3
+x 3
- +x2
4 x 5
x
- + + +
1
-x 1
3 ( )ln -x 3
1
2
( )ln - +x2
4 x 5 5 ( )arctan -x 2=
line :=
"PMMAT2|174666|Bedná, Martin |zk|ESF M-HPS HOSP [sem 2]"
, ,zadani pro "Bedná, Martin " 174666
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|174933|Benda, Vladislav |zk|ESF M-EKT EKON [sem 2]"
, ,zadani pro "Benda, Vladislav " 174933
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|172164|Beníková, Petra |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Beníková, Petra " 172164
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|174769|Blaha, Robert |zk|ESF M-HPS FP [sem 2]"
, ,zadani pro "Blaha, Robert " 174769
Vyjdrete jako elementarni funkci integral z
(5*x^4-39*x^3+124*x^2-176*x+78)/((x-2)^2*(x-3)*(x^2-6*x+18))
d
- + - +5 x4
39 x3
124 x2
176 x 78
( )-x 2 2
( )-x 3 ( )- +x2
6 x 18
x =
d+ +
1
( )-x 2 2
2
-x 3
+3 x 1
- +x2
6 x 18
x =
- + + +
1
-x 2
2 ( )ln -x 3
3
2
( )ln - +x2
6 x 18
10
3
arctan -
x
3
1
:=line "PMMAT2|151092|Cífka, Michal |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Cífka, Michal " 151092
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|171784|Dianika, Róbert |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Dianika, Róbert " 171784
Vyjdrete jako elementarni funkci integral z
((3*x^2-5*x+3)*x)/((x-1)^2*(x^2-2*x+2))
=d
x ( )- +3 x2
5 x 3
( )-x 1 2
( )- +x2
2 x 2
x d+ +
1
( )-x 1 2
2
-x 1
+x 2
- +x2
2 x 2
x =
- + + +
1
-x 1
2 ( )ln -x 1
1
2
( )ln - +x2
2 x 2 3 ( )arctan -x 1
:=line "PMMAT2|136915|Doleel, Tomá |zk|ESF B-HPS NH [sem 4]"
, ,zadani pro "Doleel, Tomá " 136915
Vyjdrete jako elementarni funkci integral z
(5*x^4-37*x^3+122*x^2-201*x+135)/((x-2)^2*(x-1)*(x^2-6*x+13))
d
- + - +5 x4
37 x3
122 x2
201 x 135
( )-x 2 2
( )-x 1 ( )- +x2
6 x 13
x =
d+ +
1
( )-x 2 2
3
-x 1
+2 x 2
- +x2
6 x 13
x =
- + + +
1
-x 2
3 ( )ln -x 1 ( )ln - +x2
6 x 13 4 arctan -
x
2
3
2
:=line "PMMAT2|171845|Fajtová, Veronika |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Fajtová, Veronika " 171845
Vyjdrete jako elementarni funkci integral z
(4*x^4-18*x^3+28*x^2-16*x+4)/((x-2)^2*(x-1)*(x^2-2*x+2))
d
2 ( )- + - + +9 x3
14 x2
8 x 2 2 x4
( )-x 2 2
( )-x 1 ( )- +x2
2 x 2
x =
d+ +
2
( )-x 2 2
2
-x 1
+2 x 2
- +x2
2 x 2
x =
- + + +
2
-x 2
2 ( )ln -x 1 ( )ln - +x2
2 x 2 4 ( )arctan -x 1
:=line "PMMAT2|172168|Ferák, Ondrej |zk|ESF B-HPS NH [sem 2]"
, ,zadani pro "Ferák, Ondrej " 172168
Vyjdrete jako elementarni funkci integral z
(5*x^3-33*x^2+81*x-72)/((x-3)^2*(x^2-6*x+18))
=d
- + -5 x3
33 x2
81 x 72
( )-x 3 2
( )- +x2
6 x 18
x d+ +
1
( )-x 3 2
2
-x 3
+3 x 2
- +x2
6 x 18
x =
- + + +
1
-x 3
2 ( )ln -x 3
3
2
( )ln - +x2
6 x 18
11
3
arctan -
x
3
1
:=line "PMMAT2|172186|Florová, Zuzana |zk|ESF B-HPS RRS [sem 2]"
, ,zadani pro "Florová, Zuzana " 172186
Vyjdrete jako elementarni funkci integral z
(3*x^4-9*x^3+13*x^2-7*x-4)/((x-1)^2*(x-2)*(x^2-2*x+5))
=d
- + - -3 x4
9 x3
13 x2
7 x 4
( )-x 1 2
( )-x 2 ( )- +x2
2 x 5
x d+ +
1
( )-x 1 2
2
-x 2
+x 2
- +x2
2 x 5
x
- + + +
1
-x 1
2 ( )ln -x 2
1
2
( )ln - +x2
2 x 5
3
2
arctan -
x
2
1
2
=
:=line "PMMAT2|135083|Havlita, Luká |zk|ESF B-HPS NH [sem 2]"
, ,zadani pro "Havlita, Luká "135083
Vyjdrete jako elementarni funkci integral z
(2*x^3-2*x^2-x+3)/((x-1)^2*(x^2-2*x+2))
=d
- - +2 x3
2 x2
x 3
( )-x 1 2
( )- +x2
2 x 2
x d+ +
2
( )-x 1 2
1
-x 1
+x 1
- +x2
2 x 2
x =
- + + +
2
-x 1
( )ln -x 1
1
2
( )ln - +x2
2 x 2 2 ( )arctan -x 1
:=line "PMMAT2|171776|Holasová, Pavla |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Holasová, Pavla " 171776
Vyjdrete jako elementarni funkci integral z
(4*x^4-18*x^3+28*x^2-16*x+4)/((x-2)^2*(x-1)*(x^2-2*x+2))
d
2 ( )- + - + +9 x3
14 x2
8 x 2 2 x4
( )-x 2 2
( )-x 1 ( )- +x2
2 x 2
x =
d+ +
2
( )-x 2 2
2
-x 1
+2 x 2
- +x2
2 x 2
x =
- + + +
2
-x 2
2 ( )ln -x 1 ( )ln - +x2
2 x 2 4 ( )arctan -x 1
:=line "PMMAT2|171762|Hurníková, Tereza |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Hurníková, Tereza " 171762
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2| 99517|Charvát, Ondej |zk|ESF B-HPS RRS [sem 2]"
, ,zadani pro "Charvát, Ondej " 99517
Vyjdrete jako elementarni funkci integral z
(6*x^4-44*x^3+128*x^2-211*x+196)/((x-3)^2*(x-2)*(x^2-2*x+10))
d
- + - +6 x4
44 x3
128 x2
211 x 196
( )-x 3 2
( )-x 2 ( )- +x2
2 x 10
x =
d+ +
1
( )-x 3 2
3
-x 2
+3 x 3
- +x2
2 x 10
x =
- + + +
1
-x 3
3 ( )ln -x 2
3
2
( )ln - +x2
2 x 10 2 arctan -
x
3
1
3
line "PMMAT2|174783|Jakubcová, Simona |zk|ESF M-HPS HOSP [\:=
sem 2]"
, ,zadani pro "Jakubcová, Simona " 174783
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2| 73899|Jurek, Daniel |zk|ESF B-HPS VEK [sem 6]"
, ,zadani pro "Jurek, Daniel " 73899
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|171933|Kamenská, Katarína |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Kamenská, Katarína " 171933
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|170527|Kantor, Ondej |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Kantor, Ondej " 170527
Vyjdrete jako elementarni funkci integral z
(3*x^4-9*x^3+13*x^2-7*x-4)/((x-1)^2*(x-2)*(x^2-2*x+5))
=d
- + - -3 x4
9 x3
13 x2
7 x 4
( )-x 1 2
( )-x 2 ( )- +x2
2 x 5
x d+ +
1
( )-x 1 2
2
-x 2
+x 2
- +x2
2 x 5
x
- + + +
1
-x 1
2 ( )ln -x 2
1
2
( )ln - +x2
2 x 5
3
2
arctan -
x
2
1
2
=
line :=
"PMMAT2|174836|Kapoun, Vítzslav |zk|ESF M-HPS VEK [sem 2]"
, ,zadani pro "Kapoun, Vítzslav " 174836
Vyjdrete jako elementarni funkci integral z
(4*x^4-18*x^3+28*x^2-16*x+4)/((x-2)^2*(x-1)*(x^2-2*x+2))
d
2 ( )- + - + +9 x3
14 x2
8 x 2 2 x4
( )-x 2 2
( )-x 1 ( )- +x2
2 x 2
x =
d+ +
2
( )-x 2 2
2
-x 1
+2 x 2
- +x2
2 x 2
x =
- + + +
2
-x 2
2 ( )ln -x 1 ( )ln - +x2
2 x 2 4 ( )arctan -x 1
line :=
"PMMAT2|174675|Kedro, Milan |zk|ESF M-HPS HOSP [sem 2]"
, ,zadani pro "Kedro, Milan " 174675
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|191617|Klimková, Jana |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Klimková, Jana " 191617
Vyjdrete jako elementarni funkci integral z
(5*x^3-22*x^2+40*x-28)/((x-2)^2*(x^2-4*x+8))
=d
- + -5 x3
22 x2
40 x 28
( )-x 2 2
( )- +x2
4 x 8
x d+ +
1
( )-x 2 2
3
-x 2
+2 x 3
- +x2
4 x 8
x =
- + + +
1
-x 2
3 ( )ln -x 2 ( )ln - +x2
4 x 8
7
2
arctan -
x
2
1
line :=
"PMMAT2|174818|Kopr, Eduard |zk|ESF M-HPS HOSP [sem 2]"
, ,zadani pro "Kopr, Eduard " 174818
Vyjdrete jako elementarni funkci integral z
(2*x^3-2*x^2-x+3)/((x-1)^2*(x^2-2*x+2))
=d
- - +2 x3
2 x2
x 3
( )-x 1 2
( )- +x2
2 x 2
x d+ +
2
( )-x 1 2
1
-x 1
+x 1
- +x2
2 x 2
x =
- + + +
2
-x 1
( )ln -x 1
1
2
( )ln - +x2
2 x 2 2 ( )arctan -x 1
line :=
"PMMAT2|174678|Koíková, Irena |zk|ESF M-EKM POH [sem 2]"
, ,zadani pro "Koíková, Irena " 174678
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|174797|Kozáková, Barbora |zk|ESF M-HPS RRS [sem 2]"
, ,zadani pro "Kozáková, Barbora " 174797
Vyjdrete jako elementarni funkci integral z
(5*x^4-29*x^3+66*x^2-74*x+38)/((x-2)^2*(x-1)*(x^2-4*x+5))
=d
- + - +5 x4
29 x3
66 x2
74 x 38
( )-x 2 2
( )-x 1 ( )- +x2
4 x 5
x d+ +
2
( )-x 2 2
3
-x 1
+2 x 3
- +x2
4 x 5
x
- + + +
2
-x 2
3 ( )ln -x 1 ( )ln - +x2
4 x 5 7 ( )arctan -x 2=
:=line "PMMAT2| 78782|Kozel, Petr |zk|ESF B-HPS RRS [sem 4]"
, ,zadani pro "Kozel, Petr " 78782
Vyjdrete jako elementarni funkci integral z
(3*x^4-19*x^3+44*x^2-26*x-38)/((x-2)^2*(x-3)*(x^2-4*x+13))
d
- + - -3 x4
19 x3
44 x2
26 x 38
( )-x 2 2
( )-x 3 ( )- +x2
4 x 13
x =
d+ +
2
( )-x 2 2
1
-x 3
+2 x 1
- +x2
4 x 13
x =
- + + +
2
-x 2
( )ln -x 3 ( )ln - +x2
4 x 13
5
3
arctan -
x
3
2
3
:=line "PMMAT2| 99730|Krková, Marie |zk|ESF B-HPS NH [sem 2]"
, ,zadani pro "Krková, Marie "99730
Vyjdrete jako elementarni funkci integral z
(2*x^4-7*x^3+12*x^2-2*x-23)/((x-1)^2*(x-3)*(x^2-2*x+10))
d
- + - -2 x4
7 x3
12 x2
2 x 23
( )-x 1 2
( )-x 3 ( )- +x2
2 x 10
x =
d+ +
1
( )-x 1 2
1
-x 3
+x 1
- +x2
2 x 10
x =
- + + +
1
-x 1
( )ln -x 3
1
2
( )ln - +x2
2 x 10
2
3
arctan -
x
3
1
3
:=line "PMMAT2|173143|Kuerová, Petra |zk|ESF M-HPS FP [sem 2]"
, ,zadani pro "Kuerová, Petra " 173143
Vyjdrete jako elementarni funkci integral z
(2*x^4-7*x^3+12*x^2-2*x-23)/((x-1)^2*(x-3)*(x^2-2*x+10))
d
- + - -2 x4
7 x3
12 x2
2 x 23
( )-x 1 2
( )-x 3 ( )- +x2
2 x 10
x =
d+ +
1
( )-x 1 2
1
-x 3
+x 1
- +x2
2 x 10
x =
- + + +
1
-x 1
( )ln -x 3
1
2
( )ln - +x2
2 x 10
2
3
arctan -
x
3
1
3
line :=
"PMMAT2|172059|Kudlová, Monika |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Kudlová, Monika " 172059
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|171779|Kusák, Roman |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Kusák, Roman " 171779
Vyjdrete jako elementarni funkci integral z
(4*x^4-26*x^3+70*x^2-78*x+2)/((x-2)^2*(x-3)*(x^2-4*x+13))
d
2 ( )- + - + +13 x3
35 x2
39 x 1 2 x4
( )-x 2 2
( )-x 3 ( )- +x2
4 x 13
x =
d+ +
2
( )-x 2 2
2
-x 3
+2 x 2
- +x2
4 x 13
x =
- + + +
2
-x 2
2 ( )ln -x 3 ( )ln - +x2
4 x 13 2 arctan -
x
3
2
3
:=line "PMMAT2|172078|Lízalová, Eva |zk|ESF B-HPS RRS [sem 2]"
, ,zadani pro "Lízalová, Eva " 172078
Vyjdrete jako elementarni funkci integral z
(2*x^4-8*x^3+12*x^2-x-10)/((x-1)^2*(x-2)*(x^2-4*x+8))
=d
- + - -2 x4
8 x3
12 x2
x 10
( )-x 1 2
( )-x 2 ( )- +x2
4 x 8
x d+ +
1
( )-x 1 2
1
-x 2
+x 1
- +x2
4 x 8
x
- + + +
1
-x 1
( )ln -x 2
1
2
( )ln - +x2
4 x 8
3
2
arctan -
x
2
1=
:=line "PMMAT2|174665|Lorenc, Jan |zk|ESF M-EKM POH [sem 2]"
, ,zadani pro "Lorenc, Jan " 174665
Vyjdrete jako elementarni funkci integral z
(4*x^4-11*x^3+15*x^2-5*x-11)/((x-1)^2*(x-2)*(x^2-2*x+5))
=d
- + - -4 x4
11 x3
15 x2
5 x 11
( )-x 1 2
( )-x 2 ( )- +x2
2 x 5
x d+ +
2
( )-x 1 2
3
-x 2
+x 3
- +x2
2 x 5
x
- + + +
2
-x 1
3 ( )ln -x 2
1
2
( )ln - +x2
2 x 5 2 arctan -
x
2
1
2
=
:=line "PMMAT2| 99655|Malík, David |zk|ESF M-EKM POH [sem 6]"
, ,zadani pro "Malík, David "99655
Vyjdrete jako elementarni funkci integral z
(6*x^4-53*x^3+182*x^2-308*x+233)/((x-3)^2*(x-1)*(x^2-6*x+10))
d
- + - +6 x4
53 x3
182 x2
308 x 233
( )-x 3 2
( )-x 1 ( )- +x2
6 x 10
x =
d+ +
1
( )-x 3 2
3
-x 1
+3 x 3
- +x2
6 x 10
x =
- + + +
1
-x 3
3 ( )ln -x 1
3
2
( )ln - +x2
6 x 10 12 ( )arctan -x 3
:=line "PMMAT2|137128|Markusík, David |zk|ESF M-HPS FP [sem 4]"
, ,zadani pro "Markusík, David " 137128
Vyjdrete jako elementarni funkci integral z
(6*x^4-53*x^3+182*x^2-308*x+233)/((x-3)^2*(x-1)*(x^2-6*x+10))
d
- + - +6 x4
53 x3
182 x2
308 x 233
( )-x 3 2
( )-x 1 ( )- +x2
6 x 10
x =
d+ +
1
( )-x 3 2
3
-x 1
+3 x 3
- +x2
6 x 10
x =
- + + +
1
-x 3
3 ( )ln -x 1
3
2
( )ln - +x2
6 x 10 12 ( )arctan -x 3
:=line "PMMAT2|100118|Miklas, David |zk|ESF B-HPS FP [sem 6]"
, ,zadani pro "Miklas, David "100118
Vyjdrete jako elementarni funkci integral z
(4*x^4-30*x^3+92*x^2-112*x+12)/((x-2)^2*(x-3)*(x^2-6*x+18))
d
2 ( )- + - + +15 x3
46 x2
56 x 6 2 x4
( )-x 2 2
( )-x 3 ( )- +x2
6 x 18
x =
d+ +
2
( )-x 2 2
2
-x 3
+2 x 2
- +x2
6 x 18
x =
- + + +
2
-x 2
2 ( )ln -x 3 ( )ln - +x2
6 x 18
8
3
arctan -
x
3
1
line :=
"PMMAT2|137816|Mlynka, Jaroslav |zk|ESF M-HPS HOSP [sem 4]"
, ,zadani pro "Mlynka, Jaroslav " 137816
Vyjdrete jako elementarni funkci integral z
(2*x^3-2*x^2-x+3)/((x-1)^2*(x^2-2*x+2))
=d
- - +2 x3
2 x2
x 3
( )-x 1 2
( )- +x2
2 x 2
x d+ +
2
( )-x 1 2
1
-x 1
+x 1
- +x2
2 x 2
x =
- + + +
2
-x 1
( )ln -x 1
1
2
( )ln - +x2
2 x 2 2 ( )arctan -x 1
line :=
"PMMAT2|107842|Navrkal, Ondej |zk|ESF M-EKM POH [sem 2]"
, ,zadani pro "Navrkal, Ondej " 107842
Vyjdrete jako elementarni funkci integral z
(6*x^4-53*x^3+182*x^2-308*x+233)/((x-3)^2*(x-1)*(x^2-6*x+10))
d
- + - +6 x4
53 x3
182 x2
308 x 233
( )-x 3 2
( )-x 1 ( )- +x2
6 x 10
x =
d+ +
1
( )-x 3 2
3
-x 1
+3 x 3
- +x2
6 x 10
x =
- + + +
1
-x 3
3 ( )ln -x 1
3
2
( )ln - +x2
6 x 10 12 ( )arctan -x 3
line :=
"PMMAT2|174963|Novotný, Michal |zk|ESF M-HPS RRS [sem 2]"
, ,zadani pro "Novotný, Michal " 174963
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|171864|Odehnal, Martin |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Odehnal, Martin " 171864
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|174734|Ohnheisrová, Iveta |zk|ESF M-HPS HOSP [sem 2]"
, ,zadani pro "Ohnheisrová, Iveta " 174734
Vyjdrete jako elementarni funkci integral z
(4*x^4-22*x^3+46*x^2-46*x+22)/((x-2)^2*(x-1)*(x^2-4*x+5))
d
2 ( )- + - + +11 x3
23 x2
23 x 11 2 x4
( )-x 2 2
( )-x 1 ( )- +x2
4 x 5
x =
d+ +
2
( )-x 2 2
2
-x 1
+2 x 2
- +x2
4 x 5
x =
- + + +
2
-x 2
2 ( )ln -x 1 ( )ln - +x2
4 x 5 6 ( )arctan -x 2
:=line "PMMAT2|172037|Petrovi, Martin |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Petrovi, Martin " 172037
Vyjdrete jako elementarni funkci integral z
(4*x^4-26*x^3+70*x^2-78*x+2)/((x-2)^2*(x-3)*(x^2-4*x+13))
d
2 ( )- + - + +13 x3
35 x2
39 x 1 2 x4
( )-x 2 2
( )-x 3 ( )- +x2
4 x 13
x =
d+ +
2
( )-x 2 2
2
-x 3
+2 x 2
- +x2
4 x 13
x =
- + + +
2
-x 2
2 ( )ln -x 3 ( )ln - +x2
4 x 13 2 arctan -
x
3
2
3
:=line "PMMAT2| 99620|Petík, Martin |zk|ESF M-HPS FP [sem 4]"
, ,zadani pro "Petík, Martin " 99620
Vyjdrete jako elementarni funkci integral z
(4*x^4-18*x^3+28*x^2-16*x+4)/((x-2)^2*(x-1)*(x^2-2*x+2))
d
2 ( )- + - + +9 x3
14 x2
8 x 2 2 x4
( )-x 2 2
( )-x 1 ( )- +x2
2 x 2
x =
d+ +
2
( )-x 2 2
2
-x 1
+2 x 2
- +x2
2 x 2
x =
- + + +
2
-x 2
2 ( )ln -x 1 ( )ln - +x2
2 x 2 4 ( )arctan -x 1
line :=
"PMMAT2|171888|Podhradský, Juraj |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Podhradský, Juraj " 171888
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|170290|Pokorný, Frantiek |zk|ESF M-EKM POH [sem 2]"
, ,zadani pro "Pokorný, Frantiek " 170290
Vyjdrete jako elementarni funkci integral z
(2*x^4-7*x^3+12*x^2-2*x-23)/((x-1)^2*(x-3)*(x^2-2*x+10))
d
- + - -2 x4
7 x3
12 x2
2 x 23
( )-x 1 2
( )-x 3 ( )- +x2
2 x 10
x =
d+ +
1
( )-x 1 2
1
-x 3
+x 1
- +x2
2 x 10
x =
- + + +
1
-x 1
( )ln -x 3
1
2
( )ln - +x2
2 x 10
2
3
arctan -
x
3
1
3
:=line "PMMAT2|134691|Potoková, Zuzana |zk|ESF M-HPS FP [sem 2]"
, ,zadani pro "Potoková, Zuzana " 134691
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line "PMMAT2|174793|Primová, Andrea |zk|ESF M-EKT EKON [s\:=
em 2]"
, ,zadani pro "Primová, Andrea " 174793
Vyjdrete jako elementarni funkci integral z
(4*x^4-23*x^3+51*x^2-55*x+27)/((x-2)^2*(x-1)*(x^2-4*x+5))
=d
- + - +4 x4
23 x3
51 x2
55 x 27
( )-x 2 2
( )-x 1 ( )- +x2
4 x 5
x d+ +
1
( )-x 2 2
2
-x 1
+2 x 2
- +x2
4 x 5
x
- + + +
1
-x 2
2 ( )ln -x 1 ( )ln - +x2
4 x 5 6 ( )arctan -x 2=
line :=
"PMMAT2|171836|Prodlalová, Linda |zk|ESF B-HPS VEK [sem 2]"
, ,zadani pro "Prodlalová, Linda " 171836
Vyjdrete jako elementarni funkci integral z
(3*x^4-19*x^3+44*x^2-26*x-38)/((x-2)^2*(x-3)*(x^2-4*x+13))
d
- + - -3 x4
19 x3
44 x2
26 x 38
( )-x 2 2
( )-x 3 ( )- +x2
4 x 13
x =
d+ +
2
( )-x 2 2
1
-x 3
+2 x 1
- +x2
4 x 13
x =
- + + +
2
-x 2
( )ln -x 3 ( )ln - +x2
4 x 13
5
3
arctan -
x
3
2
3
:=line "PMMAT2|171818|Rojko, Andrej |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Rojko, Andrej " 171818
Vyjdrete jako elementarni funkci integral z
(4*x^4-15*x^3+16*x^2+15*x-56)/((x-1)^2*(x-3)*(x^2-2*x+10))
d
- + + -4 x4
15 x3
16 x2
15 x 56
( )-x 1 2
( )-x 3 ( )- +x2
2 x 10
x =
d+ +
2
( )-x 1 2
1
-x 3
+3 x 2
- +x2
2 x 10
x =
- + + +
2
-x 1
( )ln -x 3
3
2
( )ln - +x2
2 x 10
5
3
arctan -
x
3
1
3
:=line "PMMAT2|171756|Ryek, Matou |zk|ESF B-HPS VEK [sem 2]"
, ,zadani pro "Ryek, Matou " 171756
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|174809|Slezák, Martin |zk|ESF M-EKM POH [sem 2]"
, ,zadani pro "Slezák, Martin "174809
Vyjdrete jako elementarni funkci integral z
(4*x^3-16*x^2+24*x-8)/((x-2)^2*(x^2-4*x+8))
=d
4 ( )- + - +4 x2
6 x 2 x3
( )-x 2 2
( )- +x2
4 x 8
x d+ +
2
( )-x 2 2
2
-x 2
+2 x 2
- +x2
4 x 8
x =
- + + +
2
-x 2
2 ( )ln -x 2 ( )ln - +x2
4 x 8 3 arctan -
x
2
1
:=line "PMMAT2|171885|Slezáková, Petra |zk|ESF B-HPS VEK [sem 2]"
, ,zadani pro "Slezáková, Petra " 171885
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|171931|Staro, Richard |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "Staro, Richard " 171931
Vyjdrete jako elementarni funkci integral z
(4*x^4-19*x^3+27*x^2-7*x-9)/((x-1)^2*(x-3)*(x^2-4*x+5))
=d
- + - -4 x4
19 x3
27 x2
7 x 9
( )-x 1 2
( )-x 3 ( )- +x2
4 x 5
x d+ +
1
( )-x 1 2
3
-x 3
+x 3
- +x2
4 x 5
x
- + + +
1
-x 1
3 ( )ln -x 3
1
2
( )ln - +x2
4 x 5 5 ( )arctan -x 2=
:=line "PMMAT2|172095|Steiger, Zdenk |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Steiger, Zdenk " 172095
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|174905|Stratil, Martin |zk|ESF M-EKT EKON [sem 2]"
, ,zadani pro "Stratil, Martin "174905
Vyjdrete jako elementarni funkci integral z
(4*x^4-18*x^3+28*x^2-16*x+4)/((x-2)^2*(x-1)*(x^2-2*x+2))
d
2 ( )- + - + +9 x3
14 x2
8 x 2 2 x4
( )-x 2 2
( )-x 1 ( )- +x2
2 x 2
x =
d+ +
2
( )-x 2 2
2
-x 1
+2 x 2
- +x2
2 x 2
x =
- + + +
2
-x 2
2 ( )ln -x 1 ( )ln - +x2
2 x 2 4 ( )arctan -x 1
:=line "PMMAT2|174905|Stratil, Martin |zk|ESF M-HPS HOSP [sem 2]"
, ,zadani pro "Stratil, Martin "174905
Vyjdrete jako elementarni funkci integral z
(4*x^4-18*x^3+28*x^2-16*x+4)/((x-2)^2*(x-1)*(x^2-2*x+2))
d
2 ( )- + - + +9 x3
14 x2
8 x 2 2 x4
( )-x 2 2
( )-x 1 ( )- +x2
2 x 2
x =
d+ +
2
( )-x 2 2
2
-x 1
+2 x 2
- +x2
2 x 2
x =
- + + +
2
-x 2
2 ( )ln -x 1 ( )ln - +x2
2 x 2 4 ( )arctan -x 1
line :=
"PMMAT2|172083|Svobodová, Veronika |zk|ESF M-HPS FP [sem 2]"
, ,zadani pro "Svobodová, Veronika " 172083
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|174671|afáová, Monika |zk|ESF M-HPS FP [sem 2]"
, ,zadani pro "afáová, Monika " 174671
Vyjdrete jako elementarni funkci integral z
(4*x^3-16*x^2+24*x-8)/((x-2)^2*(x^2-4*x+8))
=d
4 ( )- + - +4 x2
6 x 2 x3
( )-x 2 2
( )- +x2
4 x 8
x d+ +
2
( )-x 2 2
2
-x 2
+2 x 2
- +x2
4 x 8
x =
- + + +
2
-x 2
2 ( )ln -x 2 ( )ln - +x2
4 x 8 3 arctan -
x
2
1
line :=
"PMMAT2| 99492|amlová, Markéta |zk|ESF M-HPS RRS [sem 6]"
, ,zadani pro "amlová, Markéta " 99492
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|172194|auerová, Ludmila |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "auerová, Ludmila " 172194
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|172149|erý, Martin |zk|ESF B-HPS FP [sem 2]"
, ,zadani pro "erý, Martin " 172149
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|170179|mídová, Lucie |zk|ESF M-EKM POH [sem 2]"
, ,zadani pro "mídová, Lucie " 170179
Vyjdrete jako elementarni funkci integral z
(4*x^3-7*x^2+5*x-1)/((x-1)^2*(x^2-2*x+2))
=d
- + -4 x3
7 x2
5 x 1
( )-x 1 2
( )- +x2
2 x 2
x d+ +
1
( )-x 1 2
3
-x 1
+x 3
- +x2
2 x 2
x =
- + + +
1
-x 1
3 ( )ln -x 1
1
2
( )ln - +x2
2 x 2 4 ( )arctan -x 1
:=line "PMMAT2|171979|astná, Pavlína |zk|ESF B-HPS VEK [sem 2]"
, ,zadani pro "astná, Pavlína " 171979
Vyjdrete jako elementarni funkci integral z
(5*x^4-39*x^3+124*x^2-176*x+78)/((x-2)^2*(x-3)*(x^2-6*x+18))
d
- + - +5 x4
39 x3
124 x2
176 x 78
( )-x 2 2
( )-x 3 ( )- +x2
6 x 18
x =
d+ +
1
( )-x 2 2
2
-x 3
+3 x 1
- +x2
6 x 18
x =
- + + +
1
-x 2
2 ( )ln -x 3
3
2
( )ln - +x2
6 x 18
10
3
arctan -
x
3
1
line :=
"PMMAT2|106163|várová, Jana |zk|ESF M-EKT EKON [sem 2]"
, ,zadani pro "várová, Jana " 106163
Vyjdrete jako elementarni funkci integral z
(4*x^4-25*x^3+78*x^2-63*x-20)/((x-1)^2*(x-2)*(x^2-6*x+18))
d
- + - -4 x4
25 x3
78 x2
63 x 20
( )-x 1 2
( )-x 2 ( )- +x2
6 x 18
x =
d+ +
2
( )-x 1 2
3
-x 2
+x 1
- +x2
6 x 18
x =
- + + +
2
-x 1
3 ( )ln -x 2
1
2
( )ln - +x2
6 x 18
4
3
arctan -
x
3
1
line :=
"PMMAT2|172008|Tomková, Hana |zk|ESF B-HPS VEK [sem 2]"
, ,zadani pro "Tomková, Hana " 172008
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
line :=
"PMMAT2|171930|Turcsányi, Richard |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Turcsányi, Richard " 171930
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|171975|Turková, Lenka |zk|ESF B-HPS RRS [sem 2]"
, ,zadani pro "Turková, Lenka " 171975
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2| 65353|Valentová, Jitka |zk|ESF M-HPS VEK [sem 4]"
, ,zadani pro "Valentová, Jitka " 65353
Vyjdrete jako elementarni funkci integral z
(3*x^4-9*x^3+13*x^2-7*x-4)/((x-1)^2*(x-2)*(x^2-2*x+5))
=d
- + - -3 x4
9 x3
13 x2
7 x 4
( )-x 1 2
( )-x 2 ( )- +x2
2 x 5
x d+ +
1
( )-x 1 2
2
-x 2
+x 2
- +x2
2 x 5
x
- + + +
1
-x 1
2 ( )ln -x 2
1
2
( )ln - +x2
2 x 5
3
2
arctan -
x
2
1
2
=
line :=
"PMMAT2|171857|Valentová, Lenka |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Valentová, Lenka " 171857
Vyjdrete jako elementarni funkci integral z
(6*x^4-46*x^3+128*x^2-162*x+98)/((x-3)^2*(x-1)*(x^2-4*x+5))
d
2 ( )- + - + +23 x3
64 x2
81 x 49 3 x4
( )-x 3 2
( )-x 1 ( )- +x2
4 x 5
x =
d+ +
2
( )-x 3 2
3
-x 1
+3 x 3
- +x2
4 x 5
x =
- + + +
2
-x 3
3 ( )ln -x 1
3
2
( )ln - +x2
4 x 5 9 ( )arctan -x 2
:=line "PMMAT2|174790|Váa, Vladislav |zk|ESF M-HPS FP [sem 2]"
, ,zadani pro "Váa, Vladislav " 174790
Vyjdrete jako elementarni funkci integral z
(4*x^4-19*x^3+27*x^2-7*x-9)/((x-1)^2*(x-3)*(x^2-4*x+5))
=d
- + - -4 x4
19 x3
27 x2
7 x 9
( )-x 1 2
( )-x 3 ( )- +x2
4 x 5
x d+ +
1
( )-x 1 2
3
-x 3
+x 3
- +x2
4 x 5
x
- + + +
1
-x 1
3 ( )ln -x 3
1
2
( )ln - +x2
4 x 5 5 ( )arctan -x 2=
line :=
"PMMAT2|174973|Vdovec, Milan |zk|ESF M-EKM POH [sem 2]"
, ,zadani pro "Vdovec, Milan " 174973
Vyjdrete jako elementarni funkci integral z
(4*x^3-7*x^2+5*x-1)/((x-1)^2*(x^2-2*x+2))
=d
- + -4 x3
7 x2
5 x 1
( )-x 1 2
( )- +x2
2 x 2
x d+ +
1
( )-x 1 2
3
-x 1
+x 3
- +x2
2 x 2
x =
- + + +
1
-x 1
3 ( )ln -x 1
1
2
( )ln - +x2
2 x 2 4 ( )arctan -x 1
:=line "PMMAT2|106541|Vegrichtová, Marta |zk|ESF M-HPS FP [sem 2]"
, ,zadani pro "Vegrichtová, Marta " 106541
Vyjdrete jako elementarni funkci integral z
(4*x^4-26*x^3+70*x^2-78*x+2)/((x-2)^2*(x-3)*(x^2-4*x+13))
d
2 ( )- + - + +13 x3
35 x2
39 x 1 2 x4
( )-x 2 2
( )-x 3 ( )- +x2
4 x 13
x =
d+ +
2
( )-x 2 2
2
-x 3
+2 x 2
- +x2
4 x 13
x =
- + + +
2
-x 2
2 ( )ln -x 3 ( )ln - +x2
4 x 13 2 arctan -
x
3
2
3
:=line "PMMAT2|171976|Virglová, Lucie |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Virglová, Lucie "171976
Vyjdrete jako elementarni funkci integral z
(4*x^3-7*x^2+5*x-1)/((x-1)^2*(x^2-2*x+2))
=d
- + -4 x3
7 x2
5 x 1
( )-x 1 2
( )- +x2
2 x 2
x d+ +
1
( )-x 1 2
3
-x 1
+x 3
- +x2
2 x 2
x =
- + + +
1
-x 1
3 ( )ln -x 1
1
2
( )ln - +x2
2 x 2 4 ( )arctan -x 1
line "PMMAT2|174214|Vojtková, Ludmila |zk|ESF M-EKM POH [s\:=
em 2]"
, ,zadani pro "Vojtková, Ludmila " 174214
Vyjdrete jako elementarni funkci integral z
(2*x^4-8*x^3+12*x^2-x-10)/((x-1)^2*(x-2)*(x^2-4*x+8))
=d
- + - -2 x4
8 x3
12 x2
x 10
( )-x 1 2
( )-x 2 ( )- +x2
4 x 8
x d+ +
1
( )-x 1 2
1
-x 2
+x 1
- +x2
4 x 8
x
- + + +
1
-x 1
( )ln -x 2
1
2
( )ln - +x2
4 x 8
3
2
arctan -
x
2
1=
:=line "PMMAT2|172170|Vravko, Matej |zk|ESF B-HPS RRS [sem 2]"
, ,zadani pro "Vravko, Matej " 172170
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=
:=line "PMMAT2|171839|Zlato, Michal |zk|ESF B-EKM POH [sem 2]"
, ,zadani pro "Zlato, Michal "171839
Vyjdrete jako elementarni funkci integral z
(4*x^4-18*x^3+28*x^2-16*x+4)/((x-2)^2*(x-1)*(x^2-2*x+2))
d
2 ( )- + - + +9 x3
14 x2
8 x 2 2 x4
( )-x 2 2
( )-x 1 ( )- +x2
2 x 2
x =
d+ +
2
( )-x 2 2
2
-x 1
+2 x 2
- +x2
2 x 2
x =
- + + +
2
-x 2
2 ( )ln -x 1 ( )ln - +x2
2 x 2 4 ( )arctan -x 1
:=line "PMMAT2|174990|Zubatý, Adam |zk|ESF M-HPS FP [sem 2]"
, ,zadani pro "Zubatý, Adam " 174990
Vyjdrete jako elementarni funkci integral z
(6*x^3-39*x^2+99*x-81)/((x-3)^2*(x^2-6*x+18))
=d
3 ( )- + - +13 x2
33 x 27 2 x3
( )-x 3 2
( )- +x2
6 x 18
x d+ +
3
( )-x 3 2
3
-x 3
+3 x 3
- +x2
6 x 18
x
- + + +
3
-x 3
3 ( )ln -x 3
3
2
( )ln - +x2
6 x 18 4 arctan -
x
3
1=