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

Solving integrals/ x^2+8x^4

Integral of x^2+8x^4 dx

The solution

You have entered [src]

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

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

Integral(x^2 + 8*x^4, (x, 0, -2))

Detail solution

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

$\frac{x^{3} \left(24 x^{2} + 5\right)}{15}$
Add the constant of integration:

$\frac{x^{3} \left(24 x^{2} + 5\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(24 x^{2} + 5\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-808 
-----
  15

$$- \frac{808}{15}$$

-808 
-----
  15

$$- \frac{808}{15}$$

-808/15

Numerical answer [src]

-53.8666666666667

-53.8666666666667

The graph

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

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Integral of x^2+8x^4 dx

Limits of integration:

The graph:

Piecewise:

The solution