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Limit of the function:
e^(-x^2)/x
Graphing y =:
e^(-x^2)/x
Identical expressions
e^(-x^ two)/x
e to the power of ( minus x squared ) divide by x
e to the power of ( minus x to the power of two) divide by x
e(-x2)/x
e-x2/x
e^(-x²)/x
e to the power of (-x to the power of 2)/x
e^-x^2/x
e^(-x^2) divide by x
e^(-x^2)/xdx
Similar expressions
e^(x^2)/x

Solving integrals/ e^(-x^2)/x

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

The solution

You have entered [src]

$$\int\limits_{0}^{1} \frac{e^{- x^{2}}}{x}\, dx$$

Integral(E^(-x^2)/x, (x, 0, 1))

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

Plot the graph f(x)

The answer [src]

       / pi*I\
     Ei\e    /
oo + ---------
         2

$$\infty + \frac{\operatorname{Ei}{\left(e^{i \pi} \right)}}{2}$$

       / pi*I\
     Ei\e    /
oo + ---------
         2

$$\infty + \frac{\operatorname{Ei}{\left(e^{i \pi} \right)}}{2}$$

oo + Ei(exp_polar(pi*i))/2

Numerical answer [src]

43.6921463343444

43.6921463343444

The graph

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution