In doing math I try not to memorize shortcuts/simplifications, but instead understand what's happening. When studying integrals, my professor gave out a few "simplifications" for us to use on problems; most of which I have been able to figure out, except one. I just cannot seem to figure out the relationship given, please help clarify/explain. Thankyou.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int(\sqrt{a^2-u^2})du[/tex] = [tex]\left(\frac{u}{2}\right)[/tex][tex]\times[/tex][tex]\left(\sqrt{a^2-u^2}\right)[/tex] + [tex]\left(\frac{a^2}{2}\right)[/tex][tex]\times[/tex][tex]\left(sin^{-1}\left(\frac{u}{a}\right)\right)[/tex] + C

I have tried:

- u substitution

- trig substitution

- IBP

*It could be my steps, maybe I'm just doing the intermediates wrong.

**it took a really long time to put that formula in

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# Simplification of an integral please explain

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