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Math Help - help integrating

  1. #1
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    help integrating

    What do I use for u, du, v, and dv?

    integrate (x^3)lnx dx
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Morgan82 View Post
    What do I use for u, du, v, and dv?

    integrate (x^3)lnx dx
    Here's a useful acronym in determining what to let u be when applying integration by parts:

    L - ogarithms
    I - nverse trig
    P - polynomials
    E - exponential
    T - rig

    Using this, what is u?
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  3. #3
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    Quote Originally Posted by Morgan82 View Post
    What do I use for u, du, v, and dv?

    integrate (x^3)lnx dx
    for \int vu' = uv - \int v'u

    make v = x^3

    and u' = \ln(x)

    Find v' and u
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  4. #4
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    Are you sure? I think v=\ln x would work better.
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    Quote Originally Posted by Scott H View Post
    Are you sure? I think v=\ln x would work better.
    True  \frac{d}{dx} \left( \ln(x)\right) =\frac{1}{x}

    I meant to write that, thanks!
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  6. #6
    MHF Contributor Drexel28's Avatar
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    \int x^3 \ln(x)\:dx. Let z=\ln(x)\implies dx=e^z\:dz to get  \int x^3\ln(x)\:\overbrace{\longmapsto}_{z=\ln(x)}\int z e^{4z}\:dz. Easier now, huh?
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