Integration Problem

**xfriendsonfirex** · February 15th 2010, 12:58 PM

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

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.

**General** · February 15th 2010, 01:12 PM

Originally Posted by xfriendsonfirex

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

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.

$\int \frac{x^{2}+3x+7}{\sqrt{x}}dx=\int \frac{x^2}{\sqrt{x}} dx+\int 3\frac{x}{\sqrt{x}} \,\ dx + \int \frac{7}{\sqrt{x}}dx$
$=\int x^{\frac{3}{2}}dx+3\int x^{\frac{1}{2}}dx+7\int x^{\frac{-1}{2}}dx$ .

**xfriendsonfirex** · February 15th 2010, 01:17 PM

Sweet, got it. Thanks for all your help General within the past few days. You've been a lifesaver!

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