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Similar expressions
2x^2(3x+1)

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

The solution

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

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

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

Detail solution

Rewrite the integrand:

$2 x^{2} \left(3 x - 1\right) = 6 x^{3} - 2 x^{2}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 6 x^{3}\, dx = 6 \int x^{3}\, dx$
  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: $\frac{3 x^{4}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x^{2}\right)\, dx = - 2 \int x^{2}\, dx$
  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: $- \frac{2 x^{3}}{3}$
The result is: $\frac{3 x^{4}}{2} - \frac{2 x^{3}}{3}$
Now simplify:

$\frac{x^{3} \left(9 x - 4\right)}{6}$
Add the constant of integration:

$\frac{x^{3} \left(9 x - 4\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(9 x - 4\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/6

$$\frac{5}{6}$$

5/6

$$\frac{5}{6}$$

5/6

Numerical answer [src]

0.833333333333333

0.833333333333333

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

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

Limits of integration:

The graph:

Piecewise:

The solution