Esercizi sugli integrali
Esercizio 1. Risolvi i seguenti integrali indeniti:
1. Z 1
(3 + 5x) 6 dx [− 1
25(3 + 5x) 5 + c]
2. Z √
x + 2dx [ 2( √
x + 2) 3
3 + c]
3. Z 1
√
42x + 1 dx [ 2( √
42x + 1) 3
3 + c]
4. Z x p
3 − 2x 2 dx [− 1
6 p(3 − 2x 2 ) 3 + c]
5. Z x
√ 2 − 3x 2 dx [− 1
3
√ 2 − 3x 2 + c]
6. Z x 3
√ 1 − x 4 dx [− 1 2 √
1 − x 4 + c]
7. Z
sin 5 (x) · cos(x)dx [ 1
6 sin 6 (x) + c]
8. Z log(x)
x dx [ 1 2 log 2(x) + c]
9. Z 1 x · 1
log(x) dx [log[log(x)| + c]
10. Z
3x · e x
2dx [ 3
2 e x
2+ c]
Esercizio 2. Risolvi i seguenti integrali deniti:
1. Z 1 0
x 3 dx [ 1
4 ] 2. Z 2
0
3x 2 dx [8]
3. Z 5
−1
7dx [42]
4. Z 1
−1
4x 2 dx [ 8
3 ] 5. Z 4
2
1
x 3 dx [ 3
32 ] 6. Z 4
0
x 2 − 4x + 4 dx [ 16
3 ] 7. Z 4
−4
−x 2 + 16 dx [ 256
3 ] 8. Z 3
1
1
2 x 3 − 13
4 x 2 + 6x − 9 4
dx [ 4
3 ] 9. Z 1
−3
(x + 1) 3 dx [0]
10. Z 4 0
√ xdx [ 16
3 ]
1
11. Z 8 0
√
3x 2 dx [ 96
5 ] 12. Z 2
0
x
(x 2 + 2) 3 dx [ 1
18 ] 13. Z 1
−1
1
x − 3 dx [− log(2)]
14. Z 1 0
1
2x − 3 dx [− log(3)
2 ] 15. Z 1
−1
e −3x dx [ e 3 − e −3
3 ]
16. Z
12−
12e 2x dx [ e 2 − 1
2e ] 17. Z 2
1
xe x
2dx [ 1
2 e(e 3 − 1)]
18. Z
π40
sin(x)dx [1 −
√ 2 2 ] 19. Z
π3π 6