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

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

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integral of (e^{1/x})/x

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the nonelementary integral:

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

= - Ei (u)

Substitute back

u = \frac{1}{x}

= - Ei (\frac{1}{x})

Add a constant to the solution

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

f (x) = 4 x + 65, (4, 9)

y = x, y = (x - 3), (3, 5.3)

\frac{\partial}{\partial y} (x^{\frac{1}{2}} y^{\frac{3}{2}})

\int_{0}^{y^{3}} x e^{- \frac{x}{y}} d x

\int \frac{24}{1 - cos ( 3 x )} d x

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