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Identical expressions
x^ four + two x^2- one
x to the power of 4 plus 2x squared minus 1
x to the power of four plus two x squared minus one
x4+2x2-1
x⁴+2x²-1
x to the power of 4+2x to the power of 2-1
x^4+2x^2-1dx
Similar expressions
x^4+2x^2+1
x^4-2x^2-1

Integral of x^4+2x^2-1 dx

The solution

You have entered [src]

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

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

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

Detail solution

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

$\frac{x^{5}}{5} + \frac{2 x^{3}}{3} - x+ \mathrm{constant}$

The answer is:

$\frac{x^{5}}{5} + \frac{2 x^{3}}{3} - x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                      
 |                               5      3
 | / 4      2    \              x    2*x 
 | \x  + 2*x  - 1/ dx = C - x + -- + ----
 |                              5     3  
/

$$\int \left(\left(x^{4} + 2 x^{2}\right) - 1\right)\, dx = C + \frac{x^{5}}{5} + \frac{2 x^{3}}{3} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

292
---
 15

$$\frac{292}{15}$$

292
---
 15

$$\frac{292}{15}$$

292/15

Numerical answer [src]

19.4666666666667

19.4666666666667

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

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Integral of x^4+2x^2-1 dx

Limits of integration:

The graph:

Piecewise:

The solution