Difficult Integral

**dats13** · February 8th 2010, 06:13 PM

I have tried many different ways of solving this integral but always seem to get stuck. Any help would be greatly appreciated.

**tonio** · February 8th 2010, 06:31 PM

Originally Posted by dats13

I have tried many different ways of solving this integral but always seem to get stuck. Any help would be greatly appreciated.

$\int \frac{x}{\sqrt{(x-6)(3-x)}}\,dx=$ $\int \frac{x}{\sqrt{-x^2+9x-18}}\,dx=\frac{1}{2}\int\frac{-2x+9}{\sqrt{-x^2+9x-18}}\,dx-\frac{9}{2}\int\frac{dx}{\sqrt{-\left(x-\frac{9}{2}\right)^2+\frac{9}{4}}}$ .

The first integral above is a root, and the second one an arcsine.

Tonio

**dats13** · February 12th 2010, 06:57 AM

Thanks for the help. I finally solved it thanks to your input.

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