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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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