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

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

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫01e−xx dx\int\limits_{0}^{1} \frac{e^{- x}}{\sqrt{x}}\, dx 
Integral(E^(-x)/sqrt(x), (x, 0, 1))
Detail solution

  1. Let u=xu = \sqrt{x}.

    Then let du=dx2xdu = \frac{dx}{2 \sqrt{x}} and substitute 2du2 du:

    ∫2e−u2 du\int 2 e^{- u^{2}}\, du

    1. The integral of a constant times a function is the constant times the integral of the function:

      False\text{False}

        ErfRule(a=-1, b=0, c=0, context=exp(-_u**2), symbol=_u)

      So, the result is: πerf⁡(u)\sqrt{\pi} \operatorname{erf}{\left(u \right)}

    Now substitute uu back in:

    πerf⁡(x)\sqrt{\pi} \operatorname{erf}{\left(\sqrt{x} \right)}

  2. Add the constant of integration:

    πerf⁡(x)+constant\sqrt{\pi} \operatorname{erf}{\left(\sqrt{x} \right)}+ \mathrm{constant}

The answer is:

πerf⁡(x)+constant\sqrt{\pi} \operatorname{erf}{\left(\sqrt{x} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫e−xx dx=C+πerf⁡(x)\int \frac{e^{- x}}{\sqrt{x}}\, dx = C + \sqrt{\pi} \operatorname{erf}{\left(\sqrt{x} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900100
Plot the graph f(x)
The answer [src] 
  ____       
\/ pi *erf(1)
πerf⁡(1)\sqrt{\pi} \operatorname{erf}{\left(1 \right)} 
=
= 
  ____       
\/ pi *erf(1)
πerf⁡(1)\sqrt{\pi} \operatorname{erf}{\left(1 \right)} 
sqrt(pi)*erf(1)
Numerical answer [src] 
1.49364826509427
1.49364826509427
The graph
Integral of e^(-x)/sqrt(x) dx

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

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