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Identical expressions
4x^ two -2x+ five
4x squared minus 2x plus 5
4x to the power of two minus 2x plus five
4x2-2x+5
4x²-2x+5
4x to the power of 2-2x+5
4x^2-2x+5dx
Similar expressions
4x^2-2x-5
4x^2+2x+5

Integral of 4x^2-2x+5 dx

The solution

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  1                    
  /                    
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 |  /   2          \   
 |  \4*x  - 2*x + 5/ dx
 |                     
/                      
0

$$\int\limits_{0}^{1} \left(\left(4 x^{2} - 2 x\right) + 5\right)\, dx$$

Integral(4*x^2 - 2*x + 5, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 4 x^{2}\, dx = 4 \int x^{2}\, dx$
    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: $\frac{4 x^{3}}{3}$
  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: $\frac{4 x^{3}}{3} - x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 5\, dx = 5 x$
The result is: $\frac{4 x^{3}}{3} - x^{2} + 5 x$
Now simplify:

$\frac{x \left(4 x^{2} - 3 x + 15\right)}{3}$
Add the constant of integration:

$\frac{x \left(4 x^{2} - 3 x + 15\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(4 x^{2} - 3 x + 15\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

16/3

$$\frac{16}{3}$$

16/3

$$\frac{16}{3}$$

16/3

Numerical answer [src]

5.33333333333333

5.33333333333333

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

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Integral of 4x^2-2x+5 dx

Limits of integration:

The graph:

Piecewise:

The solution