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

The integral of (e^x)/((x+1)^2) is -(e^x)/(x+1)+1/e \Ei(x+1)+C

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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