Mathematics

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


ANSWER

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


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
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