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

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

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integral of (x*e^x)/((1+x)^2)

\int \frac{x \cdot 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

= - \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

(8 x)^{4 x}

\frac{\partial}{\partial x} (2 x sin (2 y))

\frac{d}{d x} (A x cos (x) + B cos (x))

x \to 1 lim (\frac{1}{x - 1})

\frac{1}{2 s + 1}

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