Mister Exam

Other calculators

2xe^(x^2)
Solving integrals/ 2xe^(x^2)

Integral of 2xe^(x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |       / 2\   
 |       \x /   
 |  2*x*e     dx
 |              
/               
0
∫012xex2 dx\int\limits_{0}^{1} 2 x e^{x^{2}}\, dx
Simplify
Detail solution

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

    ∫2xex2 dx=2∫xex2 dx\int 2 x e^{x^{2}}\, dx = 2 \int x e^{x^{2}}\, dx

    1. Let u=ex2u = e^{x^{2}}.

      Then let du=2xex2dxdu = 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 \frac{1}{2}\, 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:

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

    So, the result is: ex2e^{x^{2}}

  2. Add the constant of integration:

    ex2+constante^{x^{2}}+ \mathrm{constant}

The answer is:

ex2+constante^{x^{2}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                        
 |                         
 |      / 2\           / 2\
 |      \x /           \x /
 | 2*x*e     dx = C + e    
 |                         
/
ex2e^{x^2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
-1 + e
2 (e2−12)2\,\left({{e}\over{2}}-{{1}\over{2}}\right) 
=
= 
-1 + e
−1+e-1 + e
Simplify
Numerical answer [src] 
1.71828182845905
1.71828182845905
The graph
Integral of 2xe^(x^2) dx

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

    © Mister Exam – Calculator