Integral Calculus Question 399
Question: $ \int_{{}}^{{}}{\frac{\cos ecx}{\log \tan \frac{x}{2}}\ dx=} $
Options:
A) $ \log ( \log \tan \frac{x}{2} )+c $
B) $ 2\log ( \log \tan \frac{x}{2} )+c $
C) $ \frac{1}{2}\log ( \log \tan \frac{x}{2} )+c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ \log \tan \frac{x}{2}=t\Rightarrow \frac{1}{\tan \frac{x}{2}}.\frac{1}{2}{{\sec }^{2}}\frac{x}{2},dx=dt $
$ \Rightarrow cosec,x,dx=dt, $ therefore $ \int_{{}}^{{}}{\frac{cosec,x}{\log \tan \frac{x}{2}},dx}=\int_{{}}^{{}}{\frac{1}{t}dt}=\log t+c=\log ( \log \tan \frac{x}{2} )+c $ .
BETA
