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Identical expressions
5x^ three -4x+ three
5x cubed minus 4x plus 3
5x to the power of three minus 4x plus three
5x3-4x+3
5x³-4x+3
5x to the power of 3-4x+3
5x^3-4x+3dx
Similar expressions
5x^3+4x+3
5x^3-4x-3

Solving integrals/ 5x^3-4x+3

Integral of 5x^3-4x+3 dx

The solution

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  1                    
  /                    
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 |  /   3          \   
 |  \5*x  - 4*x + 3/ dx
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/                      
0

$$\int\limits_{0}^{1} \left(5 x^{3} - 4 x + 3\right)\, dx$$

Integral(5*x^3 - 4*x + 3, (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:
  
  $\int 5 x^{3}\, dx = 5 \int x^{3}\, dx$
  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: $\frac{5 x^{4}}{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 x\right)\, dx = - \int 4 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 4 x\, dx = 4 \int x\, dx$
    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: $2 x^{2}$
  So, the result is: $- 2 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 3\, dx = 3 x$
The result is: $\frac{5 x^{4}}{4} - 2 x^{2} + 3 x$
Now simplify:

$\frac{x \left(5 x^{3} - 8 x + 12\right)}{4}$
Add the constant of integration:

$\frac{x \left(5 x^{3} - 8 x + 12\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(5 x^{3} - 8 x + 12\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                           4
 | /   3          \             2         5*x 
 | \5*x  - 4*x + 3/ dx = C - 2*x  + 3*x + ----
 |                                         4  
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

9/4

$$\frac{9}{4}$$

9/4

$$\frac{9}{4}$$

Упростить

Numerical answer [src]

2.25

2.25

The graph

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

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Integral of 5x^3-4x+3 dx

Limits of integration:

The graph:

Piecewise:

The solution