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Math Help - Quick question involving integration by parts

  1. #1
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    Quick question involving integration by parts

    Here is a solution guide to a problem;

    \int \frac {3}{2x-3} + \frac {2}{(2x-3)^5} dx
    \frac{1}{2} \int \frac {1}{u}du + 2*\frac{1}{2} \int \frac{1}{u^5} du" alt="3*\frac{1}{2} \int \frac {1}{u}du + 2*\frac{1}{2} \int \frac{1}{u^5} du" />

    The red is what I don't understand. They drew out the numerator because it was a k value, but where did the one half come from?

    Has anyone ever really been far even as decided to use even go want to do look more like?
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  2. #2
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    Has anyone ever really been far even as decided to use even go want to do look more like?
    Whhhaaaaaatttttttttttttt?
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  3. #3
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    Quote Originally Posted by maddas View Post
    Whhhaaaaaatttttttttttttt?
    I was wondering the same thing.
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Archduke01 View Post
    Here is a solution guide to a problem;

    \int \frac {3}{2x-3} + \frac {2}{(2x-3)^5} dx
    \frac{1}{2} \int \frac {1}{u}du + 2*\frac{1}{2} \int \frac{1}{u^5} du" alt="3*\frac{1}{2} \int \frac {1}{u}du + 2*\frac{1}{2} \int \frac{1}{u^5} du" />

    The red is what I don't understand. They drew out the numerator because it was a k value, but where did the one half come from?

    Has anyone ever really been far even as decided to use even go want to do look more like?
    supposing u = 2x-3

    du = 2 dx

    \therefore dx = \frac{du}{2}

    when you replace 2x-3 with u, replace dx with \frac{1}{2} du. Thats how the \frac{1}{2} comes before the integral
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  5. #5
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    Awesome, thanks bumble bro.

    PS: Iron Maiden rules.
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