# Calcule $\int$ $\frac{\left[{cos^{-1}x({\sqrt{(1-x^2)})}}\right]^{-1}}{log_e\left[1+(\frac{sin(2x \sqrt{(1-x^2)})}{\pi})\right]}$dx [closed]

I had done by trigonometric substitution.. I think there is a special way to solve questions and less work Calling $$arc.cosx = t$$ is simple, but $$log$$ cm $$\pi$$ below complicates

Indefinite integral

Who can help me, or give any suggestions already thank you!

## closed as unclear what you're asking by John B, Claude Leibovici, kimchi lover, Leucippus, Jyrki LahtonenNov 9 at 10:54

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• Sorry, but closed-form integration is more of an art than a science. In fact, if you just were to jot down some expression like this at random, it would almost certainly not have a nice closed form solution. Feel vindicated that you were able to integrate it at all, and stop worrying that there is some secret method you don't know about. – Paul Sinclair Nov 9 at 3:53