INTEGRALES INDEFINIDAS RESUELTAS
= −2
∫
1 ⋅ dx + 2 x
∫
1 ⋅ dx + 2 x +1
= −2 ⋅ Ln | x | +2 ⋅ Ln | x + 1| +2
∫
∫
1 ⋅ dx + 5 ( x + 1) 2
( x + 1) −2 ⋅ dx + 5
∫
∫
1 ⋅ dx = ( x + 1)3
( x + 1) −3 ⋅ dx =
( x + 1) −1 ( x + 1)−2 = −2 ⋅ Ln | x | +2 ⋅ Ln | x + 1| +2 +5 +k = −1 −2 = Ln
( x + 1) 2 2 5 ( x + 1) 2 4( x + 1) + 5 − − + k = Ln − +k = x2 x + 1 2( x + 1) 2 x2 2( x + 1) 2
= Ln
( x + 1) 2 4x + 9 − +k 2 x 2( x + 1) 2
115.
∫
116.
∫
117.
∫
x3 − 3 x dx 64 x
∫
6
118.
119.
∫
120.
∫
121.
∫e
122.
∫
x 2 dx ( x + 2) 2 ( x + 4) 2
x 4
6
x +1 3
x + x 7
7
dx
x +1
7
4
5
x +
14
x
15
dx e +1 x
4 3
Sol:
2 4 9 2 x − 12 x 13 + k 27 13
(
4
x 3 − Ln
(
4
))
x3 +1 + k
6 12 + 12 + 2 Ln x − 24 Ln (12 x + 1) + k x x 1
1
1
1
1− x 3 1− x 6 − + 1 − x − Ln 1 + 6 1 − x + k 2 3
dx 1− x + 3 1− x
2x
Sol:
14 3 x − 7 x 2 + 14 x 5 + k Sol: 4 14 x − 7 x + 2 3 4 5
dx
ex dx + ex − 2
5 x + 12 x+4 + Ln +k 2 x + 6x + 8 x+2
Sol: − 6
dx
x+ x 8
2
Sol: −
Sol: 6
Sol:
1 ex −1 Ln x +k 3 e +2 Sol: x − Ln (e x +1) + k
31
(
)