Mathematics

$$\displaystyle \int \dfrac{e^x (x+1)}{cos^2 (xe^x)} dx $$ is equal to 


ANSWER

$$tan (xe^x) +c$$


SOLUTION
Given,

$$\displaystyle \int \dfrac{e^x\left(x+1\right)}{\cos ^2\left(xe^x\right)}dx$$

substitute $$u=xe^x\implies du=(x+1)e^xdx$$

$$\displaystyle=\int \dfrac{1}{\cos ^2\left(u\right)}du$$

$$\displaystyle =\tan \left(u\right)$$

$$=\tan \left(xe^x\right)+C$$
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Single Correct Medium Published on 17th 09, 2020
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