Integral of (3x³-2x) dx

The solution

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  1                
  /                
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 |  /   3      \   
 |  \3*x  - 2*x/ dx
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0

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

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

Detail solution

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

$\frac{3 x^{4}}{4} - x^{2}+ \mathrm{constant}$

The answer is:

$\frac{3 x^{4}}{4} - x^{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                               4
 | /   3      \           2   3*x 
 | \3*x  - 2*x/ dx = C - x  + ----
 |                             4  
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/4

$$- \frac{1}{4}$$

-1/4

$$- \frac{1}{4}$$

-1/4

Numerical answer [src]

-0.25

-0.25

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

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Integral of (3x³-2x) dx

Limits of integration:

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The solution