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Integral of d{x}:
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Integral of 4*x^3
Integral of ln(cosx)
Integral of 2x*sinx
Derivative of:
x³(2x-1)
Identical expressions
x³(2x- one)
x³(2x minus 1)
x³(2x minus one)
x³2x-1
x³(2x-1)dx
Similar expressions
x³(2x+1)

Integral of x³(2x-1) dx

The solution

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

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

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

Detail solution

Rewrite the integrand:

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

$\frac{x^{4} \left(8 x - 5\right)}{20}$
Add the constant of integration:

$\frac{x^{4} \left(8 x - 5\right)}{20}+ \mathrm{constant}$

The answer is:

$\frac{x^{4} \left(8 x - 5\right)}{20}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                        4      5
 |  3                    x    2*x 
 | x *(2*x - 1) dx = C - -- + ----
 |                       4     5  
/

$$\int x^{3} \left(2 x - 1\right)\, dx = C + \frac{2 x^{5}}{5} - \frac{x^{4}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/20

$$\frac{3}{20}$$

3/20

$$\frac{3}{20}$$

3/20

Numerical answer [src]

0.15

0.15

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

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Identical expressions

Similar expressions

Integral of x³(2x-1) dx

Limits of integration:

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Piecewise:

The solution