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Math Help - integration by parts help

  1. #1
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    integration by parts help

    im currently trying to integrate:

    xe^(x^3) dx

    u = x dv = e^(x^3)
    du = 2dx v = e^(x^3)

    and now using integration by parts formula i get


    = ( x )( e^( x^3 ) ) - integrate[e^(x^3)2xdx]

    im a lil baffled on what to do next because i still cant integrate the bolded section! thx
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  2. #2
    MHF Contributor harish21's Avatar
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    You dont need by parts here..

    just use substitution rule and let u=x^3
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  3. #3
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    You don't use integration by parts for this integral, you use substitution.

    \displaystyle \int{x^2e^{x^3}\,dx} = \frac{1}{3}\int{3x^2e^{x^3}\,dx}

    Let \displaystyle u = x^3 so that \displaystyle \frac{du}{dx} = 3x^2 and the integral becomes

    \displaystyle \frac{1}{3}\int{e^u\,\frac{du}{dx}\,dx}

    \displaystyle = \frac{1}{3}\int{e^u\,du}

    \displaystyle = \frac{1}{3}e^u + C

    \displaystyle = \frac{1}{3}e^{x^3} + C.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by maybnxtseasn View Post
    im currently trying to integrate:

    xe^(x^3) dx

    u = x dv = e^(x^3)
    du = 2dx v = e^(x^3)
    Where did you get the idea that \displaystyle \int e^{x^3}~dx = e^{x^3} ? The value of this integral is...complicated.

    -Dan
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