_ ^ e^x [ x - ( x)] ;dx =

MCQ

$\int_{}^{} {{e^x}[\tan x - \log (\cos x)]\;dx = } $

✓
${e^x}\log (\sec x) + c$
B
${e^x}\log (\cos {\rm{ec}}x) + c$
C
${e^x}\log (\cos x) + c$
D
${e^x}\log (\sin x) + c$

✓

Answer

Correct option: A.

${e^x}\log (\sec x) + c$

a
(a)$\int_{}^{} {{e^x}[\tan x - \log (\cos x)]\,dx} = \int_{}^{} {{e^x}[\tan x + \log (\sec x)]} \,dx$
$ = {e^x}\log (\sec x) + c$
$\left\{ {{\rm{Since}}\int_{}^{} {{e^x}\left\{ {f(x) + f'(x)} \right\}dx = {e^x}f(x) + c} } \right\}$.

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