Porisma

A hint to get started

Use a shown antiderivative inside integration by parts

(i) Show that ∫x1−x2 dx=−1−x2+c\displaystyle\int\dfrac{x}{\sqrt{1-x^2}}\,dx=-\sqrt{1-x^2}+c, where cc is an arbitrary constant. marks

(ii) Hence find ∫(sin⁡−1x)x1−x2 dx\displaystyle\int(\sin^{-1}x)\dfrac{x}{\sqrt{1-x^2}}\,dx. marks

[2016/JJC/Promo/9(b)]

CJC · Review Problems · Question 5

Use part (i) for v rather than starting another substitution.

Read the worked solution