Mister Exam

Other calculators

xe-x^2
Solving integrals/ xe-x^2

Integral of xe-x^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |  /       2\   
 |  \x*E - x / dx
 |               
/                
0
∫01(−x2+ex) dx\int\limits_{0}^{1} \left(- x^{2} + e x\right)\, dx 
Integral(x*E - x^2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫(−x2) dx=−∫x2 dx\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

      So, the result is: −x33- \frac{x^{3}}{3}

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

      ∫ex dx=e∫x dx\int e x\, dx = e \int x\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      So, the result is: ex22\frac{e x^{2}}{2}

    The result is: −x33+ex22- \frac{x^{3}}{3} + \frac{e x^{2}}{2}

  2. Now simplify:

    x2(−x3+e2)x^{2} \left(- \frac{x}{3} + \frac{e}{2}\right)

  3. Add the constant of integration:

    x2(−x3+e2)+constantx^{2} \left(- \frac{x}{3} + \frac{e}{2}\right)+ \mathrm{constant}

The answer is:

x2(−x3+e2)+constantx^{2} \left(- \frac{x}{3} + \frac{e}{2}\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                      3      2
 | /       2\          x    E*x 
 | \x*E - x / dx = C - -- + ----
 |                     3     2  
/
∫(−x2+ex) dx=C−x33+ex22\int \left(- x^{2} + e x\right)\, dx = C - \frac{x^{3}}{3} + \frac{e x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
  1   E
- - + -
  3   2
−13+e2- \frac{1}{3} + \frac{e}{2} 
=
= 
  1   E
- - + -
  3   2
−13+e2- \frac{1}{3} + \frac{e}{2} 
-1/3 + E/2
Numerical answer [src] 
1.02580758089619
1.02580758089619
The graph
Integral of xe-x^2 dx

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

    © Mister Exam – Calculator