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Identical expressions
sixteen -8x^ two +x^ four
16 minus 8x squared plus x to the power of 4
sixteen minus 8x to the power of two plus x to the power of four
16-8x2+x4
16-8x²+x⁴
16-8x to the power of 2+x to the power of 4
16-8x^2+x^4dx
Similar expressions
16-8x^2-x^4
16+8x^2+x^4

Solving integrals/ 16-8x^2+x^4

Integral of 16-8x^2+x^4 dx

The solution

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  1                    
  /                    
 |                     
 |  /        2    4\   
 |  \16 - 8*x  + x / dx
 |                     
/                      
-1

$$\int\limits_{-1}^{1} \left(x^{4} + \left(16 - 8 x^{2}\right)\right)\, dx$$

Integral(16 - 8*x^2 + x^4, (x, -1, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{4}\, dx = \frac{x^{5}}{5}$
1. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 16\, dx = 16 x$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 8 x^{2}\right)\, dx = - 8 \int x^{2}\, dx$
    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: $- \frac{8 x^{3}}{3}$
  The result is: $- \frac{8 x^{3}}{3} + 16 x$
The result is: $\frac{x^{5}}{5} - \frac{8 x^{3}}{3} + 16 x$
Now simplify:

$\frac{x \left(3 x^{4} - 40 x^{2} + 240\right)}{15}$
Add the constant of integration:

$\frac{x \left(3 x^{4} - 40 x^{2} + 240\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x \left(3 x^{4} - 40 x^{2} + 240\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                          
 |                                     3    5
 | /        2    4\                 8*x    x 
 | \16 - 8*x  + x / dx = C + 16*x - ---- + --
 |                                   3     5 
/

$$\int \left(x^{4} + \left(16 - 8 x^{2}\right)\right)\, dx = C + \frac{x^{5}}{5} - \frac{8 x^{3}}{3} + 16 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

406
---
 15

$$\frac{406}{15}$$

406
---
 15

$$\frac{406}{15}$$

406/15

Numerical answer [src]

27.0666666666667

27.0666666666667

The graph

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

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Integral of 16-8x^2+x^4 dx

Limits of integration:

The graph:

Piecewise:

The solution