<s>[INST] How to find $\int\sqrt{(26x-x^2)}dx $ How do I find $\int \sqrt{(26x-x^2)} dx $
Is this an integration by parts question? 
Thanks,
--Nick
 [/INST] Integrate as follows
\begin{align}
\int \sqrt{26x-x^2} dx &=
\int \frac{\sqrt{26x-x^2}}{2(x-13)}d[(x-13)^2]\\
&=\frac12(x-13)\sqrt{26x-x^2}+ \frac{169}2\int\frac1{ \sqrt{26x-x^2}}dx\\
&= \frac12(x-13)\sqrt{26x-x^2}+\frac{169}2\sin^{-1}{\frac {x-13}{13}}+C\\
\end{align}
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