Mathematics

# $\displaystyle \int e^x \frac{x-1}{(x+1)^3}dx$ is equal to

$\displaystyle \frac{e^x }{(x+1)^2}+ C$

##### SOLUTION
$\displaystyle \int e^x \frac{x-1}{(x+1)^3}dx =\int e^x\left(\frac{(x+1)-2}{(x+1)^3}\right)dx$
$=\displaystyle \int e^x\left(\frac{1}{(x+1)^2}+\frac{-2}{(x+1)^3}\right)dx$
$=\dfrac{e^x}{(x+1)^2}+C$
Since, $\int e^x[f(x)+f'(x)]dx =e^xf(x)+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

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