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

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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

= \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

\frac{( x - 1 ) ^{2}}{x ^{2}}

\frac{t}{6}

\frac{1}{( 1 + x ^{3} )}

(3 x - 5)^{- 2}

\frac{x}{y ^{2}}

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