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Identical expressions
8x^ four -5x^ two +8x
8x to the power of 4 minus 5x squared plus 8x
8x to the power of four minus 5x to the power of two plus 8x
8x4-5x2+8x
8x⁴-5x²+8x
8x to the power of 4-5x to the power of 2+8x
8x^4-5x^2+8xdx
Similar expressions
8x^4-5x^2-8x
8x^4+5x^2+8x

Integral of 8x^4-5x^2+8x dx

The solution

You have entered [src]

  1                       
  /                       
 |                        
 |  /   4      2      \   
 |  \8*x  - 5*x  + 8*x/ dx
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(8 x + \left(8 x^{4} - 5 x^{2}\right)\right)\, dx$$

Integral(8*x^4 - 5*x^2 + 8*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:
  
  $\int 8 x\, dx = 8 \int x\, dx$
  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: $4 x^{2}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 8 x^{4}\, dx = 8 \int x^{4}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{4}\, dx = \frac{x^{5}}{5}$
    So, the result is: $\frac{8 x^{5}}{5}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 5 x^{2}\right)\, dx = - 5 \int x^{2}\, dx$
    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: $- \frac{5 x^{3}}{3}$
  The result is: $\frac{8 x^{5}}{5} - \frac{5 x^{3}}{3}$
The result is: $\frac{8 x^{5}}{5} - \frac{5 x^{3}}{3} + 4 x^{2}$
Now simplify:

$\frac{x^{2} \left(24 x^{3} - 25 x + 60\right)}{15}$
Add the constant of integration:

$\frac{x^{2} \left(24 x^{3} - 25 x + 60\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(24 x^{3} - 25 x + 60\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                                        3      5
 | /   4      2      \             2   5*x    8*x 
 | \8*x  - 5*x  + 8*x/ dx = C + 4*x  - ---- + ----
 |                                      3      5  
/

$$\int \left(8 x + \left(8 x^{4} - 5 x^{2}\right)\right)\, dx = C + \frac{8 x^{5}}{5} - \frac{5 x^{3}}{3} + 4 x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

59
--
15

$$\frac{59}{15}$$

59
--
15

$$\frac{59}{15}$$

59/15

Numerical answer [src]

3.93333333333333

3.93333333333333

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

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Identical expressions

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Integral of 8x^4-5x^2+8x dx

Limits of integration:

The graph:

Piecewise:

The solution