What is the integral of e^{1/x}x ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{1/x}x

integral

e^{\frac{1}{x}} x

\frac{1}{2} e^{\frac{1}{x}} x^{2} - \frac{1}{2} (- e^{\frac{1}{x}} x + Ei (\frac{1}{x})) + C

Solution steps

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

Apply Integration By Parts

= \frac{1}{2} e^{\frac{1}{x}} x^{2} - \int - \frac{1}{2} e^{\frac{1}{x}} d x

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

= \frac{1}{2} e^{\frac{1}{x}} x^{2} - \frac{1}{2} (- e^{\frac{1}{x}} x + Ei (\frac{1}{x}))

Add a constant to the solution

= \frac{1}{2} e^{\frac{1}{x}} x^{2} - \frac{1}{2} (- e^{\frac{1}{x}} x + Ei (\frac{1}{x})) + C

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