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Identical expressions
4x^ three -3x+ ten
4x cubed minus 3x plus 10
4x to the power of three minus 3x plus ten
4x3-3x+10
4x³-3x+10
4x to the power of 3-3x+10
4x^3-3x+10dx
Similar expressions
4x^3-3x-10
4x^3+3x+10

Solving integrals/ 4x^3-3x+10

Integral of 4x^3-3x+10 dx

The solution

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  1                     
  /                     
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 |  /   3           \   
 |  \4*x  - 3*x + 10/ dx
 |                      
/                       
0

$$\int\limits_{0}^{1} \left(4 x^{3} - 3 x + 10\right)\, dx$$

Integral(4*x^3 - 3*x + 10, (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:
  
  $\int 4 x^{3}\, dx = 4 \int x^{3}\, dx$
  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: $x^{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 x\right)\, dx = - \int 3 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x\, dx = 3 \int x\, dx$
    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: $\frac{3 x^{2}}{2}$
  So, the result is: $- \frac{3 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 10\, dx = 10 x$
The result is: $x^{4} - \frac{3 x^{2}}{2} + 10 x$
Now simplify:

$\frac{x \left(2 x^{3} - 3 x + 20\right)}{2}$
Add the constant of integration:

$\frac{x \left(2 x^{3} - 3 x + 20\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{3} - 3 x + 20\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                           2
 | /   3           \           4          3*x 
 | \4*x  - 3*x + 10/ dx = C + x  + 10*x - ----
 |                                         2  
/

$$\int \left(4 x^{3} - 3 x + 10\right)\, dx = C + x^{4} - \frac{3 x^{2}}{2} + 10 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

19/2

$$\frac{19}{2}$$

19/2

$$\frac{19}{2}$$

Упростить

Numerical answer [src]

9.5

9.5

The graph

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

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Integral of 4x^3-3x+10 dx

Limits of integration:

The graph:

Piecewise:

The solution