A Level

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

∫sin⁡−1x(1−x2)3/2 dx=\int \frac{\sin^{-1}x}{(1-x^2)^{3/2}}\,dx = (a) x1−x2sin⁡−1x+12log⁡(1−x2)+c\frac{x}{\sqrt{1-x^2}}\sin^{-1}x + \frac{1}{2}\log(1-x^2) + c (b) x1−x2sin⁡−1x−12log⁡(1−x2)+c\frac{x}{\sqrt{1-x^2}}\sin^{-1}x - \frac{1}{2}\log(1-x^2) + c (c) 11−x2sin⁡−1x−12log⁡(1−x2)+c\frac{1}{\sqrt{1-x^2}}\sin^{-1}x - \frac{1}{2}\log(1-x^2) + c (d) 11−x2sin⁡−1x+12log⁡(1−x2)+c\frac{1}{\sqrt{1-x^2}}\sin^{-1}x + \frac{1}{2}\log(1-x^2) + c

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