The integral $∫e^x(tan\, x + log\, s

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Inverse Trigonometric Functions

Question:

The integral $∫e^x(tan\, x + log\, sec\, x)dx$ is equal to :

Options:

$e^xlog\, tan\, x+C$

$e^xsec\, x+C$

$e^xlog\, sec\, x+C$

$log\, sec\, x +e^x+C$

Correct Answer:

$e^xlog\, sec\, x+C$

Explanation:

$I=∫e^x(\tan\, x + \log\, \sec\, x)dx$

$=∫e^x(f(x)+f'(x))dx$ form

here $f(x)= \log\sec x,f'(x)=\tan x$

so $I=e^x\log\sec x+C$