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 $