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A hint to get started

Integrate inverse sine using a known derivative

(i) Show that ddx1−x2=−x1−x2\dfrac d{dx}\sqrt{1-x^2}=\dfrac{-x}{\sqrt{1-x^2}}, ∣x∣<1|x|<1.

(ii) Hence find ∫sin⁡−1x dx\displaystyle\int\sin^{-1}x\,dx.

CJC · Discussion · Question 9

Use part (i) for the integral remaining after parts.

Read the worked solution