Integrate: (sin^-1x)^2

Answers (1)

Solution:

              \ \ I=int (sin^-1x)^2dx hspace0.5cmput hspace0.2cmsin^-1x=t\ \ x=sin tRightarrow dx=cos t dt\ \ I=int t^2cos t dt=t^2(sin t)-2t(-cos t)+2(-sin t)+c\ \ I=(sin^-1x)^2x+2(sin^-1x)sqrt1-x^2-2x+c

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