Mathematics

# Evaluate $\int {{e^x}\left( {\tan x - \log \,\cos \,x} \right)\,dx}$

##### SOLUTION
It is just an observation to make perfect differential;
it is in the form of  $\displaystyle \int (e^{x}(f(x))+e^{x}(\dfrac{d}{dx}f(x)))dx=e^{x}(f(x))$
$\dfrac{d}{dx}\log(\cos x)=-\tan x$
so here $f(x)=\log(\cos x)$
so,
$\displaystyle\int e^{x}(\tan x-\log \cos x)dx=e^{x}(-\log\cos x)$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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