Integral Calculus Question 121
Question: $ \int{\frac{(1+x)e^{x}}{\cot (xe^{x})}dx} $ is equal to
Options:
A) $ \log | \cos (xe^{x}) |+C $
B) $ \log | \cot (xe^{x}) |+C $
C) $ \log | sec(x{e^{-x}}) |+C $
D) $ \log | sec(xe^{x}) |+C $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Let $ I=\int{\frac{(1+x)e^{x}}{\cot (xe^{x})}}dx $ Put $ xe^{x}=t\Rightarrow (xe^{x}+e^{x})dx=dt $
$ \Rightarrow e^{x}(x+1)dx=dt $
$ \therefore ,I=\int{\frac{dt}{\cot (t)}=\log | \sec t |+C} $ $ =\log | \sec (xe^{x}) |+C $
BETA
