What is the integral of x^{-2}*e^x ?

The integral of x^{-2}*e^x is -(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

Popular >

integral of x^{-2}*e^x

\int x^{- 2} \cdot e^{x} d x

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

Solution steps

\int x^{- 2} e^{x} d x

Simplify

x^{- 2} e^{x} : \frac{e ^{x}}{x ^{2}}

= \int \frac{e ^{x}}{x ^{2}} d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int e^{- (s + 3) t} d t

\int (\frac{3}{x + 1}) d x

\int sin^{3} (y) cos^{2} (y) d y

\int \frac{1}{3 + 1 + 2 x} d x

\int \frac{4}{x ^{3}} - 5 x x d x

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