Mathematics

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

$tan (xe^x) +c$

##### 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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Integrate the function   $\displaystyle \frac {\cos x}{\sqrt {1+\sin x}}$

1 Verified Answer | Published on 17th 09, 2020

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