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

1 Answer
Noah G
May 23, 2018

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!

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