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  • Choose the correct answer integral of e^x sec(1+tanx)dx

Q24  Choose the correct answer  

          \int e ^ x \sec ( 1+ \tan x ) dx \: \: \: equals

        A ) e ^ x \cos x + C \\\\ B) e ^ x \sec x + C \\\\ C ) e ^ x \sin x + C\\\\D ) e ^ x \tan x + C

Answers (1)

best_answer

we know that,
 I =\int e^x[f(x)+f'(x)]dx = e^x[f(x)]+C
from above integral 
let 
f(x)=\sec x\Rightarrow f'(x)= \sec x.\tan x
thus, the solution of the above integral is 
I=e^x\sec x+C

Posted by

manish

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