Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/5x
Integral of sqrt(1+e^(2x))
Integral of sinx/cos2x
Integral of sqrt(1-x^2)dx
Derivative of:
x^2e^3x
Identical expressions
x^2e^3x
x squared e cubed x
x2e3x
x²e³x
x to the power of 2e to the power of 3x
x^2e^3xdx
Similar expressions
x^2*e^3*x
What you mean?
x^2*e^3*x
x^((2*e)^(3*x))
x^((2*e)^(3*x))

Solving integrals/ x^2e^3x

You entered:

x^2e^3x

What you mean?

x^2*e^3*x

x^((2*e)^(3*x))

x^((2*e)^(3*x))

Integral of x^2e^3x dx

The solution

You have entered [src]

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

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

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

Detail solution

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

$\int x x^{2} e^{3}\, dx = e^{3} \int x x^{2}\, dx$
1. Let $u = x^{2}$ .
  
  Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{u}{4}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{u}{2}\, du = \frac{\int u\, du}{2}$
    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: $\frac{u^{2}}{4}$
  Now substitute $u$ back in:
  
  $\frac{x^{4}}{4}$
So, the result is: $\frac{x^{4} e^{3}}{4}$
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  
/

$${{e^3\,x^4}\over{4}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

 3
e 
--
4

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

=

 3
e 
--
4

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

Упростить

Numerical answer [src]

5.02138423079692

5.02138423079692

The graph

Integral of x^2e^3x dx

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