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Integral of d{x}:
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Integral of cos(5x)
Derivative of:
2x^3-3
Graphing y =:
2x^3-3
Identical expressions
2x^ three - three
2x cubed minus 3
2x to the power of three minus three
2x3-3
2x³-3
2x to the power of 3-3
2x^3-3dx
Similar expressions
2x^3+3

Integral of 2x^3-3 dx

The solution

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

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

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

Detail solution

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

$\frac{x \left(x^{3} - 6\right)}{2}$
Add the constant of integration:

$\frac{x \left(x^{3} - 6\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} - 6\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$34$$

Numerical answer [src]

34.0

34.0

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

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Integral of 2x^3-3 dx

Limits of integration:

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Piecewise:

The solution