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

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

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The solution

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∫012xe−x2 dx\int\limits_{0}^{1} 2 x e^{- x^{2}}\, dx 
Integral(2*x/E^(x^2), (x, 0, 1))
Detail solution

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

    ∫2xe−x2 dx=2∫xe−x2 dx\int 2 x e^{- x^{2}}\, dx = 2 \int x e^{- x^{2}}\, dx

    1. Let u=e−x2u = e^{- x^{2}}.

      Then let du=−2xe−x2dxdu = - 2 x e^{- x^{2}} dx and substitute −du2- \frac{du}{2}:

      ∫14 du\int \frac{1}{4}\, du

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

        ∫(−12) du=−∫1 du2\int \left(- \frac{1}{2}\right)\, du = - \frac{\int 1\, du}{2}

        1. The integral of a constant is the constant times the variable of integration:

          ∫1 du=u\int 1\, du = u

        So, the result is: −u2- \frac{u}{2}

      Now substitute uu back in:

      −e−x22- \frac{e^{- x^{2}}}{2}

    So, the result is: −e−x2- e^{- x^{2}}

  2. Add the constant of integration:

    −e−x2+constant- e^{- x^{2}}+ \mathrm{constant}

The answer is:

−e−x2+constant- e^{- x^{2}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
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 | 2*x*e    dx = C - e   
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−e−x2-e^ {- x^2 }
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
     -1
1 - e
2 (12−e−12)2\,\left({{1}\over{2}}-{{e^ {- 1 }}\over{2}}\right) 
=
= 
     -1
1 - e
−1e+1- \frac{1}{e} + 1
Упростить
Numerical answer [src] 
0.632120558828558
0.632120558828558
The graph
Integral of 2*x*e^(-x^2) dx

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

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