Question

Evaluate

$\int \frac{dx}{9+16{cos}^{2}x}$

Answer 1

We have,

$\int \frac{dx}{9+16{\cos }^{2}x}$

$\Rightarrow \int \frac{dx}{3^2+{\left(4\cos x\right)}^2}$

Using formula

$\int \frac{dx}{a^2+x^2}=\frac{1}{a}{\tan }^{-1}\frac{x}{a}$

$\Rightarrow \int \frac{dx}{3^2+{\left(4\cos x\right)}^2}=\frac{1}{3}{\tan }^{-1}\left(\frac{4\cos x}{3}\right)+C$

Hence, this is the answer.