Mathematics

# $\int {{e^x}\left[ {{\mathop{\rm tanx}\nolimits} - log\left( {\cos x} \right)} \right]} dx =$

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

##### SOLUTION
$\displaystyle\int e^x\left[\tan x-log (\cos x)\right]dx$
$=\displaystyle\int e^x\left[\tan x+log (\sec x)\right]d$
$=\displaystyle\int \dfrac{d}{dx}\left\{e^xlog(\sec x)\right\}dx$
$=e^xlog (\sec x)+c$.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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