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Identical expressions
x^ eight (3x- one)^ two
x to the power of 8(3x minus 1) squared
x to the power of eight (3x minus one) to the power of two
x8(3x-1)2
x83x-12
x⁸(3x-1)²
x to the power of 8(3x-1) to the power of 2
x^83x-1^2
x^8(3x-1)^2dx
Similar expressions
x^8(3x+1)^2

Solving integrals/ x^8(3x-1)^2

Integral of x^8(3x-1)^2 dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |   8          2   
 |  x *(3*x - 1)  dx
 |                  
/                   
0

$$\int\limits_{0}^{1} x^{8} \left(3 x - 1\right)^{2}\, dx$$

Integral(x^8*(3*x - 1)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

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

$\frac{x^{9} \left(405 x^{2} - 297 x + 55\right)}{495}$
Add the constant of integration:

$\frac{x^{9} \left(405 x^{2} - 297 x + 55\right)}{495}+ \mathrm{constant}$

The answer is:

$\frac{x^{9} \left(405 x^{2} - 297 x + 55\right)}{495}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                           10    9      11
 |  8          2          3*x     x    9*x  
 | x *(3*x - 1)  dx = C - ----- + -- + -----
 |                          5     9      11 
/

$$\int x^{8} \left(3 x - 1\right)^{2}\, dx = C + \frac{9 x^{11}}{11} - \frac{3 x^{10}}{5} + \frac{x^{9}}{9}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

163
---
495

$$\frac{163}{495}$$

163
---
495

$$\frac{163}{495}$$

163/495

Numerical answer [src]

0.329292929292929

0.329292929292929

The graph

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

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Integral of x^8(3x-1)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution