Question
Prove the integration formula$$\int \sin ^{-1} x d x=x \sin ^{-1} x+\sqrt{1-x^{2}}+C$$(a) by applying integration by parts to $\int \sin ^{-1} x d x$;(b) by differentiating $\sqrt{1-x^{2}}+x \sin ^{-1} x$.
Step 1
We can rewrite the integral as $\int \sin ^{-1} x \cdot 1 d x$. Show more…
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