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Identical expressions
(8x^ three -2x)^ four
(8x cubed minus 2x) to the power of 4
(8x to the power of three minus 2x) to the power of four
(8x3-2x)4
8x3-2x4
(8x³-2x)⁴
(8x to the power of 3-2x) to the power of 4
8x^3-2x^4
(8x^3-2x)^4dx
Similar expressions
(8x^3+2x)^4

Solving integrals/ (8x^3-2x)^4

Integral of (8x^3-2x)^4 dx

The solution

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  0                 
  /                 
 |                  
 |              4   
 |  /   3      \    
 |  \8*x  - 2*x/  dx
 |                  
/                   
0

$$\int\limits_{0}^{0} \left(8 x^{3} - 2 x\right)^{4}\, dx$$

Integral((8*x^3 - 2*x)^4, (x, 0, 0))

Detail solution

Rewrite the integrand:

$\left(8 x^{3} - 2 x\right)^{4} = 4096 x^{12} - 4096 x^{10} + 1536 x^{8} - 256 x^{6} + 16 x^{4}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4096 x^{12}\, dx = 4096 \int x^{12}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{12}\, dx = \frac{x^{13}}{13}$
  So, the result is: $\frac{4096 x^{13}}{13}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4096 x^{10}\right)\, dx = - 4096 \int x^{10}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{10}\, dx = \frac{x^{11}}{11}$
  So, the result is: $- \frac{4096 x^{11}}{11}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 1536 x^{8}\, dx = 1536 \int x^{8}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{8}\, dx = \frac{x^{9}}{9}$
  So, the result is: $\frac{512 x^{9}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 256 x^{6}\right)\, dx = - 256 \int x^{6}\, dx$
  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: $- \frac{256 x^{7}}{7}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 16 x^{4}\, dx = 16 \int x^{4}\, dx$
  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: $\frac{16 x^{5}}{5}$
The result is: $\frac{4096 x^{13}}{13} - \frac{4096 x^{11}}{11} + \frac{512 x^{9}}{3} - \frac{256 x^{7}}{7} + \frac{16 x^{5}}{5}$
Now simplify:

$\frac{16 x^{5} \cdot \left(295680 x^{8} - 349440 x^{6} + 160160 x^{4} - 34320 x^{2} + 3003\right)}{15015}$
Add the constant of integration:

$\frac{16 x^{5} \cdot \left(295680 x^{8} - 349440 x^{6} + 160160 x^{4} - 34320 x^{2} + 3003\right)}{15015}+ \mathrm{constant}$

The answer is:

$\frac{16 x^{5} \cdot \left(295680 x^{8} - 349440 x^{6} + 160160 x^{4} - 34320 x^{2} + 3003\right)}{15015}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                    
 |                                                                     
 |             4                11        7       5        9         13
 | /   3      \           4096*x     256*x    16*x    512*x    4096*x  
 | \8*x  - 2*x/  dx = C - -------- - ------ + ----- + ------ + --------
 |                           11        7        5       3         13   
/

$${{4096\,x^{13}}\over{13}}-{{4096\,x^{11}}\over{11}}+{{512\,x^9 }\over{3}}-{{256\,x^7}\over{7}}+{{16\,x^5}\over{5}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Simplify

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 (8x^3-2x)^4 dx

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Piecewise:

The solution