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(3x- one)(one -2x)^ four
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Similar expressions
(3x+1)(1-2x)^4
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Integral of (3x-1)(1-2x)^4 dx

The solution

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  1                        
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 |                     4   
 |  (3*x - 1)*(1 - 2*x)  dx
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0

$$\int\limits_{0}^{1} \left(1 - 2 x\right)^{4} \left(3 x - 1\right)\, dx$$

Integral((3*x - 1)*(1 - 2*x)^4, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(1 - 2 x\right)^{4} \left(3 x - 1\right) = 48 x^{5} - 112 x^{4} + 104 x^{3} - 48 x^{2} + 11 x - 1$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 48 x^{5}\, dx = 48 \int x^{5}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{5}\, dx = \frac{x^{6}}{6}$
  So, the result is: $8 x^{6}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 112 x^{4}\right)\, dx = - 112 \int x^{4}\, dx$
  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: $- \frac{112 x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 104 x^{3}\, dx = 104 \int x^{3}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $26 x^{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 48 x^{2}\right)\, dx = - 48 \int x^{2}\, dx$
  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: $- 16 x^{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 11 x\, dx = 11 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{11 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $8 x^{6} - \frac{112 x^{5}}{5} + 26 x^{4} - 16 x^{3} + \frac{11 x^{2}}{2} - x$
Now simplify:

$\frac{x \left(80 x^{5} - 224 x^{4} + 260 x^{3} - 160 x^{2} + 55 x - 10\right)}{10}$
Add the constant of integration:

$\frac{x \left(80 x^{5} - 224 x^{4} + 260 x^{3} - 160 x^{2} + 55 x - 10\right)}{10}+ \mathrm{constant}$

The answer is:

$\frac{x \left(80 x^{5} - 224 x^{4} + 260 x^{3} - 160 x^{2} + 55 x - 10\right)}{10}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                       
 |                                                               5       2
 |                    4                  3      6       4   112*x    11*x 
 | (3*x - 1)*(1 - 2*x)  dx = C - x - 16*x  + 8*x  + 26*x  - ------ + -----
 |                                                            5        2  
/

$$\int \left(1 - 2 x\right)^{4} \left(3 x - 1\right)\, dx = C + 8 x^{6} - \frac{112 x^{5}}{5} + 26 x^{4} - 16 x^{3} + \frac{11 x^{2}}{2} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/10

$$\frac{1}{10}$$

1/10

$$\frac{1}{10}$$

1/10

Numerical answer [src]

0.1

0.1

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

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Integral of (3x-1)(1-2x)^4 dx

Limits of integration:

The graph:

Piecewise:

The solution