Mister Exam

Other calculators

Solving integrals/ x*e

Integral of x*e dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  0       
  /       
 |        
 |  x*E dx
 |        
/         
-oo
∫−∞0ex dx\int\limits_{-\infty}^{0} e x\, dx 
Integral(x*E, (x, -oo, 0))
Detail solution

  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}

  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
 |              E*x 
 | x*E dx = C + ----
 |               2  
/
∫ex dx=C+ex22\int e x\, dx = C + \frac{e x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9001
Plot the graph f(x)
The answer [src] 
-oo
−∞-\infty 
=
= 
-oo
−∞-\infty 
-oo

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

    © Mister Exam – Calculator