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

Solving integrals/ (2x^4-x^2+4)

Integral of (2x^4-x^2+4) dx

The solution

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

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

Integral(2*x^4 - x^2 + 4, (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:
  
  $\int 2 x^{4}\, dx = 2 \int x^{4}\, dx$
  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: $\frac{2 x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  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: $- \frac{x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
The result is: $\frac{2 x^{5}}{5} - \frac{x^{3}}{3} + 4 x$
Now simplify:

$\frac{x \left(6 x^{4} - 5 x^{2} + 60\right)}{15}$
Add the constant of integration:

$\frac{x \left(6 x^{4} - 5 x^{2} + 60\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x \left(6 x^{4} - 5 x^{2} + 60\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{2\,x^5}\over{5}}-{{x^3}\over{3}}+4\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

61
--
15

$${{61}\over{15}}$$

61
--
15

$$\frac{61}{15}$$

Упростить

Numerical answer [src]

4.06666666666667

4.06666666666667

The graph

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

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Integral of (2x^4-x^2+4) dx

Limits of integration:

The graph:

Piecewise:

The solution