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Math Help - Integration Problem

  1. #1
    Junior Member xfriendsonfirex's Avatar
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    Integration Problem

    \int \frac{x^{2}+3x+7}{\sqrt{x}}dx

    Would the correct way to start this problem be to bring the denominator to the numerator and distribute it, or to break the problem up, using the common denominator? I'm having difficulty with both approaches.
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by xfriendsonfirex View Post
    \int \frac{x^{2}+3x+7}{\sqrt{x}}dx

    Would the correct way to start this problem be to bring the denominator to the numerator and distribute it, or to break the problem up, using the common denominator? I'm having difficulty with both approaches.
    \int \frac{x^{2}+3x+7}{\sqrt{x}}dx=\int \frac{x^2}{\sqrt{x}} dx+\int 3\frac{x}{\sqrt{x}} \,\ dx + \int \frac{7}{\sqrt{x}}dx
    =\int x^{\frac{3}{2}}dx+3\int x^{\frac{1}{2}}dx+7\int x^{\frac{-1}{2}}dx.
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  3. #3
    Junior Member xfriendsonfirex's Avatar
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    Sweet, got it. Thanks for all your help General within the past few days. You've been a lifesaver!
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