Mister Exam

Other calculators

x*e^(4*x^2)
Solving integrals/ x*e^(4*x^2)

Integral of x*e^(4*x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |        2   
 |     4*x    
 |  x*E     dx
 |            
/             
0
$$\int\limits_{0}^{1} e^{4 x^{2}} x\, dx$$ 
Integral(x*E^(4*x^2), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                      
 |                      2
 |       2           4*x 
 |    4*x           e    
 | x*E     dx = C + -----
 |                    8  
/
$$\int e^{4 x^{2}} x\, dx = C + \frac{e^{4 x^{2}}}{8}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       4
  1   e 
- - + --
  8   8
$$- \frac{1}{8} + \frac{e^{4}}{8}$$ 
=
= 
       4
  1   e 
- - + --
  8   8
$$- \frac{1}{8} + \frac{e^{4}}{8}$$ 
-1/8 + exp(4)/8
Numerical answer [src] 
6.69976875414303
6.69976875414303
The graph
Integral of x*e^(4*x^2) dx

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

    © Mister Exam – Calculator