Mathematics

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


ANSWER

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


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
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