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Similar expressions
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Solving integrals/ x^4(5-x^2)

Integral of x^4(5-x^2) dx

The solution

You have entered [src]

  0               
  /               
 |                
 |   4 /     2\   
 |  x *\5 - x / dx
 |                
/                 
0

$$\int\limits_{0}^{0} x^{4} \left(5 - x^{2}\right)\, dx$$

Integral(x^4*(5 - x^2), (x, 0, 0))

Detail solution

Rewrite the integrand:

$x^{4} \left(5 - x^{2}\right) = - x^{6} + 5 x^{4}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{6}\right)\, dx = - \int x^{6}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{6}\, dx = \frac{x^{7}}{7}$
  So, the result is: $- \frac{x^{7}}{7}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 x^{4}\, dx = 5 \int x^{4}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{4}\, dx = \frac{x^{5}}{5}$
  So, the result is: $x^{5}$
The result is: $- \frac{x^{7}}{7} + x^{5}$
Add the constant of integration:

$- \frac{x^{7}}{7} + x^{5}+ \mathrm{constant}$

The answer is:

$- \frac{x^{7}}{7} + x^{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                            7
 |  4 /     2\           5   x 
 | x *\5 - x / dx = C + x  - --
 |                           7 
/

$$\int x^{4} \left(5 - x^{2}\right)\, dx = C - \frac{x^{7}}{7} + x^{5}$$

Simplify

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Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

The graph

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

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Integral of x^4(5-x^2) dx

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Piecewise:

The solution