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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
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 |  x*E     dx
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0
∫01ex2x dx\int\limits_{0}^{1} e^{x^{2}} x\, dx 
Integral(x*E^(x^2), (x, 0, 1))
Detail solution

  1. Let u=x2u = x^{2}.

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

    ∫eu2 du\int \frac{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}

      1. The integral of the exponential function is itself.

        ∫eu du=eu\int e^{u}\, du = e^{u}

      So, the result is: eu2\frac{e^{u}}{2}

    Now substitute uu back in:

    ex22\frac{e^{x^{2}}}{2}

  2. Add the constant of integration:

    ex22+constant\frac{e^{x^{2}}}{2}+ \mathrm{constant}

The answer is:

ex22+constant\frac{e^{x^{2}}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                   / 2\
 |    / 2\           \x /
 |    \x /          e    
 | x*E     dx = C + -----
 |                    2  
/
∫ex2x dx=C+ex22\int e^{x^{2}} x\, dx = C + \frac{e^{x^{2}}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.05.0
Plot the graph f(x)
The answer [src] 
  1   E
- - + -
  2   2
−12+e2- \frac{1}{2} + \frac{e}{2} 
=
= 
  1   E
- - + -
  2   2
−12+e2- \frac{1}{2} + \frac{e}{2} 
-1/2 + E/2
Numerical answer [src] 
0.859140914229523
0.859140914229523
The graph
Integral of x*e^(x^2) dx

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

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