Integral Calculus Question 138
Question: What is $ \int{\frac{e^{x}(1+x)}{{{\cos }^{2}}( xe^{x} )}dx} $ equal to?
Options:
A) $ xe^{x}+c $
B) $ \cos (xe^{x})+c $
C) $ \tan (xe^{x})+c $
D) $ x\cos ec(xe^{x})+c $ Where c is a constant of integration.
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let $ I=\int{\frac{e^{x}(1+x)}{{{\cos }^{2}}( xe^{x} )}dx} $ Put, $ xe^{x}=t\Rightarrow e^{x}(1+x)dx=dt $
$ \therefore I=\int{\frac{dt}{{{\cos }^{2}}t}=\int{{{\sec }^{2}}tdt=\tan t+c}} $ $ =\tan (xe^{x})+c $ where ?c? is a constant of integration.
BETA
