Integral Calculus Question 423
Question: The value of $ \int_{{}}^{{}}{e^{x}{{\sec }^{2}}(e^{x})\ dx} $ is
Options:
A) $ \tan (e^{x})+k $
B) $ \tan (e^{x})\ .\ e+k $
C) $ e^{x}\tan x+k $
D) $ \frac{\tan (e^{x})}{e^{x}}+k $
Show Answer
Answer:
Correct Answer: A
Solution:
$ I=\int_{{}}^{{}}{e^{x}{{\sec }^{2}}(e^{x}),dx} $ . Put $ e^{x}=t\Rightarrow e^{x}dx=dt $
$ \therefore ,I=\int_{{}}^{{}}{{{\sec }^{2}}t,dt=\tan t+k=\tan (e^{x})+k} $ .
BETA
