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Math Help - Calc integration using substitution

  1. #1
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    Calc integration using substitution

    Integrate: (x^2)((x^3)-1)^4)dx
    I got:
    U=(x^3)-1 then dU=((x^3)-1)dx then dU/((x^3)-1) so finally I have: Integrate ((x^2)(U^4)dU)/((x^3)-1).
    Now what?
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  2. #2
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    Dec 2008
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    Your u should be x^3-1. You derivate u, and get 3x^2dx. Your dx then becomes 1/3x^2du. Substitute into your equation and you get 1/3u^4. Integrate. You get 1/15u^5. Substitute your x^3-1 back in to get 1/5(x^3-1)^5+C.
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