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)

$\frac{1}{a}\,\tan \,\frac{ax}{2}+c$

Answer 2

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