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Math Help - U-Substitution Problem

  1. #1
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    U-Substitution Problem

    Sorry about the multitude of questions but I have a midterm on thursday! Woe is me! xD

    This U-Sub has caused me some problems, I'm not quite sure how to approach it.

    ∫xdx/(1+√x)

    If I substitute U=1+√x I get 1/2√x so that doesn't help
    and if I substitute U=x that of course turns into du=dx

    Any advice?
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Audioslavery View Post
    Sorry about the multitude of questions but I have a midterm on thursday! Woe is me! xD

    This U-Sub has caused me some problems, I'm not quite sure how to approach it.

    ∫xdx/(1+√x)

    If I substitute U=1+√x I get 1/2√x so that doesn't help
    and if I substitute U=x that of course turns into du=dx

    Any advice?

    Let u = \sqrt x, then du = \frac{1}{2 \sqrt x}dx \implies dx = du . 2 \sqrt x

    substitute this in your integral to get:

    \int x \times 2 \sqrt x \frac{1}{1+u} du

    = 2 \int \sqrt x \times \sqrt x \times \sqrt x \frac{1}{1+u} du

    = 2 \int \frac{u^3}{1+u} du

    rewrite

     \frac{u^3}{1+u} = u^2 - u + 1 - \frac{1}{1+u}

    and integrate
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