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Solving integrals/ x^5

Integral of x^5 dx

You have entered [src]

$$\int\limits_{0}^{1} x^{5}\, dx$$

Integral(x^5, (x, 0, 1))

Detail solution

The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :

$\int x^{5}\, dx = \frac{x^{6}}{6}$
Add the constant of integration:

$\frac{x^{6}}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{6}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /              
 |              6
 |  5          x 
 | x  dx = C + --
 |             6 
/

$$\int x^{5}\, dx = C + \frac{x^{6}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/6

$$\frac{1}{6}$$

1/6

$$\frac{1}{6}$$

1/6

Numerical answer [src]

0.166666666666667

0.166666666666667

The graph

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