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Derivative of:
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Graphing y =:
e^(1/x)
Limit of the function:
e^(1/x)
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e to the power of (1 divide by x)
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e^(1/x)dx

Integral of e^(1/x) dx

The solution

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  1         
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0

$$\int\limits_{0}^{1} e^{\frac{1}{x}}\, dx$$

Integral(E^(1/x), (x, 0, 1))

Detail solution

Let $u = \frac{1}{x}$ .

Then let $du = - \frac{dx}{x^{2}}$ and substitute $- du$ :

$\int \left(- \frac{e^{u}}{u^{2}}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{e^{u}}{u^{2}}\, du = - \int \frac{e^{u}}{u^{2}}\, du$
  So, the result is: $\frac{\operatorname{E}_{2}\left(- u\right)}{u}$
Now substitute $u$ back in:

$x \operatorname{E}_{2}\left(- \frac{1}{x}\right)$
Add the constant of integration:

$x \operatorname{E}_{2}\left(- \frac{1}{x}\right)+ \mathrm{constant}$

The answer is:

$x \operatorname{E}_{2}\left(- \frac{1}{x}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
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 | x ___                  /   -1 \
 | \/ E  dx = C + x*expint|2, ---|
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/

$$\int e^{\frac{1}{x}}\, dx = C + x \operatorname{E}_{2}\left(- \frac{1}{x}\right)$$

Simplify

The answer [src]

oo - Ei(1)

$$- \operatorname{Ei}{\left(1 \right)} + \infty$$

oo - Ei(1)

$$- \operatorname{Ei}{\left(1 \right)} + \infty$$

oo - Ei(1)

Numerical answer [src]

3.91470672358516e+4333645441173067313

3.91470672358516e+4333645441173067313

Use the examples entering the upper and lower limits of integration.

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Identical expressions

Integral of e^(1/x) dx

Limits of integration:

The graph:

Piecewise:

The solution