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Identical expressions
(x^ two -9x^ four)
(x squared minus 9x to the power of 4)
(x to the power of two minus 9x to the power of four)
(x2-9x4)
x2-9x4
(x²-9x⁴)
(x to the power of 2-9x to the power of 4)
x^2-9x^4
(x^2-9x^4)dx
Similar expressions
(x^2+9x^4)

Solving integrals/ (x^2-9x^4)

Integral of (x^2-9x^4) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |  / 2      4\   
 |  \x  - 9*x / dx
 |                
/                 
-1

$$\int\limits_{-1}^{1} \left(- 9 x^{4} + x^{2}\right)\, dx$$

Integral(x^2 - 9*x^4, (x, -1, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 9 x^{4}\right)\, dx = - \int 9 x^{4}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 9 x^{4}\, dx = 9 \int x^{4}\, dx$
    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: $\frac{9 x^{5}}{5}$
  So, the result is: $- \frac{9 x^{5}}{5}$
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: $- \frac{9 x^{5}}{5} + \frac{x^{3}}{3}$
Now simplify:

$\frac{x^{3} \cdot \left(5 - 27 x^{2}\right)}{15}$
Add the constant of integration:

$\frac{x^{3} \cdot \left(5 - 27 x^{2}\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \cdot \left(5 - 27 x^{2}\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                         5    3
 | / 2      4\          9*x    x 
 | \x  - 9*x / dx = C - ---- + --
 |                       5     3 
/

$${{x^3}\over{3}}-{{9\,x^5}\over{5}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-44 
----
 15

$$-{{44}\over{15}}$$

-44 
----
 15

$$- \frac{44}{15}$$

Simplify

Numerical answer [src]

-2.93333333333333

-2.93333333333333

The graph

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

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Integral of (x^2-9x^4) dx

Limits of integration:

The graph:

Piecewise:

The solution