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Integral of d{x}:
Integral of x^2*e^3x
Integral of x/(2x+3)
Integral of x^2/sqrt(x^2-25)
Integral of x^2sqrt(x^2-9)
Derivative of:
x^2*e^3x
Graphing y =:
x^2*e^3x
Identical expressions
x^ two *e^3x
x squared multiply by e cubed x
x to the power of two multiply by e cubed x
x2*e3x
x²*e³x
x to the power of 2*e to the power of 3x
x^2e^3x
x2e3x
x^2*e^3xdx
Similar expressions
x^2*e^3*x

Solving integrals/ x^2*e^3x

Integral of x^2*e^3x dx

The solution

You have entered [src]

  1           
  /           
 |            
 |   2  3     
 |  x *E *x dx
 |            
/             
0

$$\int\limits_{0}^{1} x e^{3} x^{2}\, dx$$

Integral((x^2*E^3)*x, (x, 0, 1))

Detail solution

Let $u = x^{2}$ .

Then let $du = 2 x dx$ and substitute $\frac{du e^{3}}{2}$ :

$\int \frac{u e^{3}}{2}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u\, du = \frac{e^{3} \int u\, du}{2}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u\, du = \frac{u^{2}}{2}$
  So, the result is: $\frac{u^{2} e^{3}}{4}$
Now substitute $u$ back in:

$\frac{x^{4} e^{3}}{4}$
Add the constant of integration:

$\frac{x^{4} e^{3}}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{4} e^{3}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                   4  3
 |  2  3            x *e 
 | x *E *x dx = C + -----
 |                    4  
/

$$\int x e^{3} x^{2}\, dx = C + \frac{x^{4} e^{3}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

 3
e 
--
4

$$\frac{e^{3}}{4}$$

=

 3
e 
--
4

$$\frac{e^{3}}{4}$$

exp(3)/4

Numerical answer [src]

5.02138423079692

5.02138423079692

The graph

Integral of x^2*e^3x dx

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