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Integral of d{x}:
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Integral of (3x-2)^2
Identical expressions
x^(two)*e^-3x
x to the power of (2) multiply by e to the power of minus 3x
x to the power of (two) multiply by e to the power of minus 3x
x(2)*e-3x
x2*e-3x
x^(2)e^-3x
x(2)e-3x
x2e-3x
x^2e^-3x
x^(2)*e^-3xdx
Similar expressions
x^(2)*e^+3x
What you mean?
x^2*x/e^3
x^2/e^(3*x)
x^2/e^(3*x)

You entered:

x^(2)*e^-3x

What you mean?

x^2*x/e^3

x^2/e^(3*x)

x^2/e^(3*x)

Integral of x^(2)*e^-3x dx

The solution

You have entered [src]

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

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

Detail solution

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

$\int \frac{x x^{2}}{e^{3}}\, dx = \frac{\int x x^{2}\, dx}{e^{3}}$
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: $\frac{x^{4}}{4 e^{3}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

 -3
e  
---
 4

$$\frac{1}{4 e^{3}}$$

 -3
e  
---
 4

$$\frac{1}{4 e^{3}}$$

Упростить

Numerical answer [src]

0.012446767091966

0.012446767091966

The graph

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

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What you mean?

Integral of x^(2)*e^-3x dx

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Piecewise:

The solution