Question

How do you integrate `int (2x+5)(x^2+5x)^7dx` using substitution?

Answer 1

`int(2x+5)(x^2+5x)^7dx=1/8(x^2+5x)^8+"c"`

Explanation:

We want to find `int(2x+5)(x^2+5x)^7dx=int(x^2+5x)^7(2x+5)dx`.

Let `u=x^2+5x` and `du=(2x+5)dx` and sub this into the integral to transform it to

`intu^7du=1/8u^8+"c"=1/8(x^2+5x)^8+"c"`