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Solving integrals/ x^4+2x^2-1

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

Limits of integration:

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The graph:

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Piecewise:

The solution

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-2
∫−22((x4+2x2)−1) dx\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

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x4 dx=x55\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:

        ∫2x2 dx=2∫x2 dx\int 2 x^{2}\, dx = 2 \int x^{2}\, dx

        1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

          ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

        So, the result is: 2x33\frac{2 x^{3}}{3}

      The result is: x55+2x33\frac{x^{5}}{5} + \frac{2 x^{3}}{3}

    1. The integral of a constant is the constant times the variable of integration:

      ∫(−1) dx=−x\int \left(-1\right)\, dx = - x

    The result is: x55+2x33−x\frac{x^{5}}{5} + \frac{2 x^{3}}{3} - x

  2. Add the constant of integration:

    x55+2x33−x+constant\frac{x^{5}}{5} + \frac{2 x^{3}}{3} - x+ \mathrm{constant}

The answer is:

x55+2x33−x+constant\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  
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∫((x4+2x2)−1) dx=C+x55+2x33−x\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
-2.0-1.5-1.0-0.52.00.00.51.01.5-5050
Plot the graph f(x)
The answer [src] 
292
---
 15
29215\frac{292}{15} 
=
= 
292
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 15
29215\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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