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Limit of the function:
exp(-x^2)/x
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Similar expressions
exp(x^2)/x

Integral of exp(-x^2)/x dx

The solution

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$$\int\limits_{0}^{\infty} \frac{e^{- x^{2}}}{x}\, dx$$

Integral(exp(-x^2)/x, (x, 0, oo))

Detail solution

Let $u = - x^{2}$ .

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

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

$\frac{\operatorname{Ei}{\left(- x^{2} \right)}}{2}$
Add the constant of integration:

$\frac{\operatorname{Ei}{\left(- x^{2} \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\operatorname{Ei}{\left(- x^{2} \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                     
 |                      
 |    2                 
 |  -x             /  2\
 | e             Ei\-x /
 | ---- dx = C + -------
 |  x               2   
 |                      
/

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

Simplify

The graph

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The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

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

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Identical expressions

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Integral of exp(-x^2)/x dx

Limits of integration:

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The solution