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.#