Corso di Matematica generale
ESERCIZI PROPOSTI SUL CALCOLO DI INTEGRALI INDEFINITI
Integrali immediati, per scomposizione o di semplici funzioni razionali
x dx,
2x3 +x
x2 +2
cos xdx,
2
1
√
x
2−x2 dx,
x
x2 −5 dx,
√
x
m
√
2
x 7x dx,
x
ex dx,
x8/3 dx,
x
√
8
1
cos2 x )dx,
xn dx,
xdx,
(ex +
1
x
− 2)dx,
10x dx,
√
( x + 1)dx,
x2 +7x−9
√
5 x
( sin12 x −
(1−x2 )
√ dx,
x x
x7/4 dx,
xn dx,
1
dx,
sin2 x
x4 dx,
1
x2 dx,
√
e√ x
dx,
x
√x+3 dx,
x2 −4
(1 − 2x)dx,
1−x
x dx,
x2√
+1
dx,
x x
x2 +1
x2 −4 dx,
1
cos2 x dx,
x1/n dx,
xdx,
3, 4 x−0,7 dx,
(e a − e− a )dx,
x
(x + x1 )2 dx,
(1 + e3x )2 e3x dx,
sin xdx,
x2 +x+9
x2 −9 dx,
tan xdx,
2x−1,2 dx,
x1/n dx,
x2 −4x+2
√
dx,
x
dx,
x
x−x3 ex +x2
dx,
x3
7x3 −2
x2 +4 dx,
dx,
7x dx,
xn dx,
√
(x + 1)3 xdx,
√
x
x+1
1
1+x2 dx,
(2x + 1)dx,
ax ex dx,
ax dx,
√ 1
dx,
1−x2
dx,
dx,
√
7
(
√
3
√
x2 − 4 x)
√
dx,
x
2x
1+x2 dx,
xdx,
ex
ex −1 dx,
√
(1+ x)3
√
dx,
3 x
(2x3 + 7)dx,
x4n−3 dx,
42−3x dx.
Integrali per parti
x sin 2x dx,
ln (x2 + 1) dx,
x2 e−x dx,
x cos x dx,
x2 cos xdx,
x2 ex dx,
x e−x dx,
x ax dx,
ln2 x dx,
x 3x dx,
x3 3x dx,
x3 ln x dx,
xn ln x dx,
ln x
x3
x2 sin xdx,
x cos 7x dx,
dx,
x2 ln (1 + x) dx,
x cos 3x dx.
Integrali per sostituzione
(x + 1)9 dx,
(3x)n dx,
√ 1
dx,
1−4x2
(3 − x)4 dx,
x
x2 +2
e−9x dx,
dx,
1
1+4x2 dx,
x
3x2 −1
cos 7xdx,
2x
1+x2 dx,
(6x − 7)8/3 dx.
dx,
x2
x3 +9
a−2x dx,
dx,
x
2−x2 dx,
x
x2 −2
7−8x dx,
dx,
tan 7xdx,
x4
x5 +8
dx,
sin (4x + 5)dx,
94x+5 dx,
(5x + 3)1/n dx,
tan xdx,
