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

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

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |        2   
 |     2*x    
 |  x*e     dx
 |            
/             
0
∫01xe2x2 dx\int\limits_{0}^{1} x e^{2 x^{2}}\, dx 
Integral(x*exp(2*x^2), (x, 0, 1))
Detail solution

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

    Then let du=4xdxdu = 4 x dx and substitute du4\frac{du}{4}:

    ∫eu4 du\int \frac{e^{u}}{4}\, 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: eu4\frac{e^{u}}{4}

    Now substitute uu back in:

    e2x24\frac{e^{2 x^{2}}}{4}

  2. Add the constant of integration:

    e2x24+constant\frac{e^{2 x^{2}}}{4}+ \mathrm{constant}

The answer is:

e2x24+constant\frac{e^{2 x^{2}}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                      2
 |       2           2*x 
 |    2*x           e    
 | x*e     dx = C + -----
 |                    4  
/
∫xe2x2 dx=C+e2x24\int x e^{2 x^{2}}\, dx = C + \frac{e^{2 x^{2}}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
       2
  1   e 
- - + --
  4   4
−14+e24- \frac{1}{4} + \frac{e^{2}}{4} 
=
= 
       2
  1   e 
- - + --
  4   4
−14+e24- \frac{1}{4} + \frac{e^{2}}{4} 
-1/4 + exp(2)/4
Numerical answer [src] 
1.59726402473266
1.59726402473266
The graph
Integral of x*exp(2x^2) dx

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

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