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Solving integrals/ x-x^3

Integral of x-x^3 dx

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$$\int\limits_{-1}^{1} \left(- x^{3} + x\right)\, dx$$

Integral(x - x^3, (x, -1, 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:
  
  $\int \left(- x^{3}\right)\, dx = - \int x^{3}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $- \frac{x^{4}}{4}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
The result is: $- \frac{x^{4}}{4} + \frac{x^{2}}{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

The graph

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