A) \[\frac{1}{2}\log \,\tan \left( \frac{x}{2}+\frac{\pi }{12} \right)+c\]
B) \[\frac{1}{2}\log \,\,\tan \left( \frac{x}{2}-\frac{\pi }{12} \right)+c\]
C) \[\log \,\,\tan \left( \frac{x}{2}+\frac{\pi }{12} \right)+c\]
D) \[\log \,\tan \left( \frac{x}{2}-\frac{\pi }{12} \right)+c\]
Correct Answer: A
Solution :
[a] \[\int{\frac{dx}{\cos +\sqrt{3}\sin x}=\frac{1}{2}\int{\frac{dx}{\frac{1}{2}\cos x+\frac{\sqrt{3}}{2}\sin x}}}\] \[=\frac{1}{2}\int{\frac{dx}{\cos \left( x-\frac{\pi }{3} \right)}}=\frac{1}{2}\int{\sec \left( x-\frac{\pi }{3} \right)dx}\] \[=\frac{1}{2}\log \tan \left( \frac{x}{2}-\frac{\pi }{6}+\frac{\pi }{4} \right)+c\] \[=\frac{1}{2}\log \tan \left( \frac{x}{2}+\frac{\pi }{12} \right)+c\]
You need to login to perform this action.
You will be redirected in
3 sec
