Question

$\int \frac{1}{1+\cos ax}dx$ is equal to

• A. $\cot \frac{ax}{2}+c$
• B. $\frac{1}{a}\tan \frac{ax}{2}+c$
• C. $\frac{1}{a}(\text{cosec ax - cot ax)+c}$
• D. $\frac{1}{a}(\text{cosec ax + cot ax)+c}$

Answer 1

Answer: (B)

$\int \frac{1}{1+\cos ax}dx$
$=\int \frac{dx}{2{\cos }^2(ax/2)}$
$=\frac{1}{2}\int {\sec }^2\frac{ax}{2}dx=\frac{1}{2}.\frac{\tan ax/2}{a/2}$
$=\frac{1}{a}\tan \frac{ax}{2}+c$