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

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Answer 1 · 2018-03-07T20:59:52

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

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

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

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