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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x ^{4} + 1}{x ^{2} + 1})

\frac{\partial}{\partial x} (y (e^{x^{2} - x y}))

\frac{d}{d x} (cos (e^{t a n (3 x)}))

\int 6 sin (6 x) d x

\frac{\partial}{\partial x} (e^{6})

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