I was wondering if there is a convenient way of checking if a substitution is correct or not.(adsbygoogle = window.adsbygoogle || []).push({});

For example, I tried solving for ∫(1/(a^2-x^2)dx using two different substitutions, x=acosu and x=asinu giving different solutions. I got the integral as arcsin(x/a) using x=asinu and -arccos(x/a) using x=acosu. But which one of these is the correct one and how do I tackle this sort of problem if it arises again?

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# Use of substitution for integration

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