Mathematics

Find:
$$\displaystyle \int \dfrac {xe^{x}}{(1+x)^{2}}dx$$


SOLUTION
$$y = \int \frac{xe^{x}}{(1+x)^{2}}dx$$
$$y=\int [\frac{1}{1+x}-\frac{1}{(1+x)^{2}}]dx$$
We know $$\int e^{x}[f(x)-f(x)]=e^{x}f(x)$$
then
$$y=\int e^{x}[\frac{1}{1+x}-\frac{1}{(1+x)^{2}}]dx=\frac{e^{x}}{1+x}+c$$
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Subjective Medium Published on 17th 09, 2020
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