The value of $\int \frac{\mathrm{d} x}{5+4 \cos x}$ is

$\frac{1}{3} \tan ^{-1}\left(\frac{1}{3} \tan x\right)+C$

$\frac{1}{3} \tan ^{-1}\left(\frac{1}{3} \tan \left(\frac{x}{2}\right)\right)+C$

$\frac{2}{3} \tan ^{-1}\left(\frac{1}{3} \tan x\right)+C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int \frac{\mathrm{d} x}{5+4 \cos x}

View answer and explanation

Correct option: D

\frac{2}{3} \tan ^{-1}\left(\frac{1}{3} \tan \left(\frac{x}{2}\right)\right)+C

Option D (

\frac{2}{3} \tan ^{-1}\left(\frac{1}{3} \tan \left(\frac{x}{2}\right)\right)+C

) is correct because it is the result of integrating the given expression using the tangent half-angle substitution.