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Question
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
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Solution
Let I = `int ((sin^-1 x)^(3/2))/sqrt(1 - x^2).dx`
Put sin–1x = t.
∴ `(1)/sqrt(1 - x^2).dx` = dt
∴ I = `int t^(3/2)dt`
= `t^(5/2)/(5/2) + c`
= `(2)/(5)(sin^-1x)^(5/2) + c`.
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