What is the integral of ((xe^x))/((1+x)^2) ?

The integral of ((xe^x))/((1+x)^2) is -(e^xx)/(1+x)+e^x+C

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integral of ((xe^x))/((1+x)^2)

\int \frac{( x e ^{x} )}{( 1 + x ) ^{2}} d x

- \frac{e ^{x} x}{1 + x} + e^{x} + C

Solution steps

\int \frac{x e ^{x}}{( 1 + x ) ^{2}} d x

Apply Integration By Parts

= - \frac{e ^{x} x}{1 + x} - \int - e^{x} d x

\int - e^{x} d x = - e^{x}

= - \frac{e ^{x} x}{1 + x} - (- e^{x})

Simplify

= - \frac{e ^{x} x}{1 + x} + e^{x}

Add a constant to the solution

= - \frac{e ^{x} x}{1 + x} + e^{x} + C

What is the integral of ((xe^x))/((1+x)^2) ?
The integral of ((xe^x))/((1+x)^2) is -(e^xx)/(1+x)+e^x+C