_ ^ x ;dx a^2 + b^2 ^2 x = - Vidyadip

MCQ

$\int_{}^{} {\frac{{\sin x\;dx}}{{{a^2} + {b^2}{{\cos }^2}x}}} = $

A
$\log ({a^2} + {b^2}{\cos ^2}x) + c$
B
$\frac{1}{{ab}}{\tan ^{ - 1}}\left( {\frac{{a\cos x}}{b}} \right) + c$
✓
$\frac{1}{{ab}}{\cot ^{ - 1}}\left( {\frac{{b\cos x}}{a}} \right) + c$
D
$\frac{1}{{ab}}{\cot ^{ - 1}}\left( {\frac{{a\cos x}}{b}} \right) + c$

✓

Answer

Correct option: C.

$\frac{1}{{ab}}{\cot ^{ - 1}}\left( {\frac{{b\cos x}}{a}} \right) + c$

c
(c) Put $b\cos x = t$.

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