How do you integrate $int-9x^2(-3x^3+1)^3$ using substitution?

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How do you integrate $int-9x^2(-3x^3+1)^3dx$ using substitution?

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Answer 1 · 2016-10-07T17:58:44

$(-3x^3+1)^4/4+C.$

Let us write $I=int-9x^2(-3x^3+1)^3dx.$

Sbstn. $(-3x^3+1)=y rArr -9x^2dx=dy.$ Hence,

$I=inty^3dy$

$=y^4/4$

$=(-3x^3+1)^4/4+C.$