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

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

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
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 |   x     
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∫0∞e−x2x dx\int\limits_{0}^{\infty} \frac{e^{- x^{2}}}{x}\, dx 
Integral(exp(-x^2)/x, (x, 0, oo))
Detail solution

  1. Let u=−x2u = - x^{2}.

    Then let du=−2xdxdu = - 2 x dx and substitute du2\frac{du}{2}:

    ∫eu2u du\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:

      ∫euu du=∫euu du2\int \frac{e^{u}}{u}\, du = \frac{\int \frac{e^{u}}{u}\, du}{2}

        EiRule(a=1, b=0, context=exp(_u)/_u, symbol=_u)

      So, the result is: Ei⁡(u)2\frac{\operatorname{Ei}{\left(u \right)}}{2}

    Now substitute uu back in:

    Ei⁡(−x2)2\frac{\operatorname{Ei}{\left(- x^{2} \right)}}{2}

  2. Add the constant of integration:

    Ei⁡(−x2)2+constant\frac{\operatorname{Ei}{\left(- x^{2} \right)}}{2}+ \mathrm{constant}

The answer is:

Ei⁡(−x2)2+constant\frac{\operatorname{Ei}{\left(- x^{2} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫e−x2x dx=C+Ei⁡(−x2)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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