Mister Exam

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Integral of d{x}:
Integral of y=x^2
Integral of x^2*e^(-x)
Integral of x⁴
Integral of x^2*ln(x)
Derivative of:
e^(1/x)
Graphing y =:
e^(1/x)
Limit of the function:
e^(1/x)
Identical expressions
e^(one /x)
e to the power of (1 divide by x)
e to the power of (one divide by x)
e(1/x)
e1/x
e^1/x
e^(1 divide by x)
e^(1/x)dx

Integral of e^(1/x) dx

The solution

You have entered [src]

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

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.

Other calculators

How to use it?

Identical expressions

Integral of e^(1/x) dx

Limits of integration:

The graph:

Piecewise:

The solution