^ - 1 x - ^ - 1 x ^ - 1 x + ^ - 1 x dx = - Vidyadip

MCQ

$\int {\frac{{{{\sin }^{ - 1}}x - {{\cos }^{ - 1}}x}}{{{{\sin }^{ - 1}}x + {{\cos }^{ - 1}}x}}} dx = $

✓
$\frac{4}{\pi }\left( {x{{\sin }^{ - 1}}x + \sqrt {1 - {x^2}} } \right) - x + c$
B
$\log |{\sin ^{ - 1}}x + {\cos ^{ - 1}}x| + c$
C
$\frac{4}{\pi }\left( {x{{\sin }^{ - 1}}x + \sqrt {1 - {x^2}} } \right) + c$
D
None of these

✓

Answer

Correct option: A.

$\frac{4}{\pi }\left( {x{{\sin }^{ - 1}}x + \sqrt {1 - {x^2}} } \right) - x + c$

a
$\int \frac{\sin ^{-1} x-\left(\pi / 2-\sin ^{-1} x\right)}{\pi / 2} d x$

$\left.\frac{2}{\pi} \int 2 \sin ^{-1} x-\pi / 2\right) d x$

$\frac{4}{\pi} \int \sin ^{-1} x d x-\int d x$

$\frac{4}{\pi}\left[\int x \sin ^{-1} x-\int \frac{x d x}{\sqrt{1-x^{2}}}\right]-x+c$

$\frac{4}{\pi}\left[x \sin ^{-1} x+\sqrt{1-x^{2}}\right]-x+c$

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