Question

Question #e4f3d

Answer 1

There must be a typo. This integral cannot be done by substitution.

Explanation:

That `19x` should (I assume) be `10x`.

`I = int((3x+5)dx)/(3x^2+10x+2)^(2/3)`

Let `u = 3x^2+10x+2`. The `du = (6x+10) dx = 2(3x+5) dx`

`I = 1/2 int(2(3x+5)dx)/(3x^2+10x+2)^(2/3)`

`= 1/2 int (du)/u^(2/3) = 1/2 int u^(-2/3) du = 1/2 (3u^1/3) +C`

`= 3/2 (3x^2+10x+2)^1/3 +C`