INTEGRALES INDEFINIDAS RESUELTAS
∫ (e
5x
)
+ a 5 x dx =
∫
1 5
=
61.
62.
∫e
x2 + 4 x+ 3
∫
∫
(a x − b x ) 2 dx a xbx
∫
(a x − b x ) 2 dx = a xb x
=
∫
+4 x +3
1 5 Ln a
∫
5a 5 x Ln a d x =
1 5x 1 e + ⋅ a5x + k = 5 5 Ln a
1 5x a5x e + +k 5 L a
Sol:
( x +2) dx
ex
2
5e 5 x dx +
( x + 2) dx =
1 2
∫
ex
2
+4 x +3
1 x 2 +4 x + 3 e +k 2
2( x + 2) dx =
1 x 2 +4 x +3 e +k 2 x
x
a b − Sol: b a − 2x + k La −Lb
∫
a 2 x − 2a x b x + b 2 x dx = a xbx
∫
a2x b2x x x + x x − 2 dx = a b a b
∫
ax bx x + x − 2 dx = a b
x x a x b x 1 1 a b ⋅ + ⋅ − 2x + k = + − 2 dx = a b b a a b Ln Ln b a x
x
1 1 a b = ⋅ + ⋅ − 2x + k = Ln a − Ln b b Ln b − Ln a a x
x
a b b a = − − 2x + k = Ln a − Ln b Ln a − Ln b
63.
64.
∫
ex dx 3 + 4e x
∫
ex 1 dx = x 4 3 + 4e
x
Sol:
∫
x
a b − b a − 2x + k La −Lb
1 Ln ( 3 + 4e x ) + k 4
4e x 1 dx = Ln ( 3 + 4e x ) + k x 4 3 + 4e
∫cos 5 xdx
Sol:
1 sen 5 x + k 5
∫cos 5 xdx = 5 ∫5 cos 5 xdx = ∫ f ' ( x ) ⋅ cos f ( x )dx = sen f ( x ) + k = 5 sen 5 x + k 1
65.
∫
sen
x dx 3
Sol: − 3 cos
10
x +k 3
1