Please show the integration of $(x^3)/((x^4+7)^8)dx$ step by step?

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Answer 1 · 2018-05-23T04:55:56

We have

$I = int x^3/(x^4 + 7)^8 dx$

Let $u = x^4 + 7dx$ . Then $du = 4x^3 dx$ and $dx = (du)/(4x^3)$

$I = int x^3/u^8 * (du)/(4x^3)$

$I = 1/4int u^-8 du$

$I = 1/4(-1/7u^-7) + C$

$I = -1/28(x^4 + 7)^-7 +C$

Hopefully this helps!

Please show the integration of (x^3)/((x^4+7)^8)dx(x^3)/((x^4+7)^8)dx step by step?