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Solving integrals/ x^3+x

Integral of x^3+x dx

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$$\int\limits_{0}^{2} \left(x^{3} + x\right)\, dx$$

Integral(x^3 + x, (x, 0, 2))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
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:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                         
 |                    2    4
 | / 3    \          x    x 
 | \x  + x/ dx = C + -- + --
 |                   2    4 
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$${{x^4}\over{4}}+{{x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$6$$

Simplify

Numerical answer [src]

6.0

6.0

The graph

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