JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \frac{\mathrm{d} x}{a^2 \cos ^2 x+b^2 \sin ^2 x}(a, b>0)

is equal to

View answer and explanation

Correct option: C

\frac{1}{a b} \tan ^{-1}\left(\left(\frac{b}{a}\right) \tan x\right)+C

Option C (

\frac{{1}}{{a b}} \tan ^{-1}\left(\left(\frac{{b}}{{a}}\right) \tan x\right)+C

) is correct because dividing by

\cos^2 x

and substituting

t = \tan x

leads to an arctangent integral.

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