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Integral of d{x}:
Integral of cosx^2
Integral of sinh(x)
Integral of xcos(nx)
Integral of 1/x^n
Graphing y =:
x^4-4x^2
Identical expressions
x^ four -4x^ two
x to the power of 4 minus 4x squared
x to the power of four minus 4x to the power of two
x4-4x2
x⁴-4x²
x to the power of 4-4x to the power of 2
x^4-4x^2dx
Similar expressions
x^4+4x^2

Integral of x^4-4x^2 dx

The solution

You have entered [src]

  1               
  /               
 |                
 |  / 4      2\   
 |  \x  - 4*x / dx
 |                
/                 
0

$$\int\limits_{0}^{1} \left(x^{4} - 4 x^{2}\right)\, dx$$

Integral(x^4 - 4*x^2, (x, 0, 1))

Detail solution

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

$\frac{x^{3} \left(3 x^{2} - 20\right)}{15}$
Add the constant of integration:

$\frac{x^{3} \left(3 x^{2} - 20\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(3 x^{2} - 20\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

-17 
----
 15

$$- \frac{17}{15}$$

-17 
----
 15

$$- \frac{17}{15}$$

-17/15

Numerical answer [src]

-1.13333333333333

-1.13333333333333

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

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Integral of x^4-4x^2 dx

Limits of integration:

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The solution