Integral of arcsin(x)/(x^2) I did the integration by parts and got this expression, but then I am stuck on how to take it further. I tried substituting u=1-x^2, but then I had to do a partial fraction decomposition (which I did not take). Any hints or help would be very appreciated!
Take $x = \sin u$ initially to get simple integral.
$$\int u \csc( u )\cot( u) du= -u\csc( u) + \int \csc (u) du\\
= -u \csc (u) +\ln|\cot( u )-\csc (u)| + c.$$
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