Let, I = ∫sin^ 1 x√(1 x^2) dx Put #160; #160; #160; #160; #160; #160; #160; #160; #160; sin^ 1 x = t 1√(1 x^2) dx = ...

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Integration of Trigonometric Functions

Solve: ∫sin...

Question

Solve: $\int \frac{{sin}^{- 1} x}{\sqrt{1 - x^{2}}}$

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Solution

$L e t, I = \int \frac{{sin}^{- 1} x}{\sqrt{1 - x^{2}}} d x$

Put ${sin}^{- 1} x = t$

$⟹ \frac{1}{\sqrt{1 - x^{2}}} d x = d t$

$∴ I = \int t d t$

$I = \frac{t^{2}}{2} + c = \frac{({sin}^{- 1} x)^{2}}{2} + c$ (Ans)

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