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Math Help - Integration by Parts

  1. #1
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    Integration by Parts

    I'm sure how to go about solving this integral:

    ∫cos(ln(2x))dx

    Could someone explain how to set it up to use integration by parts?
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Integration by Parts

    Use u=\text{ln}(2x)
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  3. #3
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    Re: Integration by Parts

    Quote Originally Posted by MaxJasper View Post
    Use u=\text{ln}(2x)
    Okay, that'll give me du = 1/x dx which I cannot substitute back into the original equation.
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  4. #4
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    Re: Integration by Parts

    Quote Originally Posted by Preston019 View Post
    Okay, that'll give me du = 1/x dx which I cannot substitute back into the original equation.
    u = \ln(2x)

    x = \frac{e^u}{2}

    dx = \frac{e^u}{2} \, du

    substitute ...

    \int \cos(u) \cdot \frac{e^u}{2} \, du

    now perform the integration by parts ...
    Thanks from Preston019
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  5. #5
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    Re: Integration by Parts

    Quote Originally Posted by skeeter View Post
    u = \ln(2x)

    x = \frac{e^u}{2}

    dx = \frac{e^u}{2} \, du

    substitute ...

    \int \cos(u) \cdot \frac{e^u}{2} \, du

    now perform the integration by parts ...
    Oooooooohhh! Okay, that helped so much. Thanks!
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