Integral of (x²-5x⁴)dx dx

The solution

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 5 x^{4}\right)\, dx = - 5 \int x^{4}\, dx$
  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: $- x^{5}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
The result is: $- x^{5} + \frac{x^{3}}{3}$
Add the constant of integration:

$- x^{5} + \frac{x^{3}}{3}+ \mathrm{constant}$

The answer is:

$- x^{5} + \frac{x^{3}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                            3
 | / 2      4\           5   x 
 | \x  - 5*x / dx = C - x  + --
 |                           3 
/

$$\int \left(- 5 x^{4} + x^{2}\right)\, dx = C - x^{5} + \frac{x^{3}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2920/3

$$- \frac{2920}{3}$$

-2920/3

$$- \frac{2920}{3}$$

-2920/3

Numerical answer [src]

-973.333333333333

-973.333333333333

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

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Integral of (x²-5x⁴)dx dx

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The solution