Integral Calculus Question 373
Question: $ \int{e^{x}(1+\tan x+{{\tan }^{2}}x)dx=} $
[Karnataka CET 1999]
Options:
A) $ e^{x}\sin x+c $
B) $ e^{x}\cos x+c $
C) $ e^{x}\tan x+c $
D) $ e^{x}\sec x+c $
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Answer:
Correct Answer: C
Solution:
$ I=\int{e^{x}(1+\tan x+{{\tan }^{2}}x})dx $
Þ $ \int{e^{x}(1+\tan x+{{\tan }^{2}}x)dx=\int{e^{x}(\tan x+{{\sec }^{2}}x)},dx.} $ $ I=e^{x}\tan x+c $ $ (\because ,\int{e^{x}[f(x)+{f}’(x)]+x=e^{x}f(x)+c}). $
BETA
