Integral of x^e dx

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

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

Detail solution

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

$\int x^{e}\, dx = \frac{x^{1 + e}}{1 + e}$
Add the constant of integration:

$\frac{x^{1 + e}}{1 + e}+ \mathrm{constant}$

The answer is:

$\frac{x^{1 + e}}{1 + e}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |              1 + E
 |  E          x     
 | x  dx = C + ------
 |             1 + E 
/

$$\int x^{e}\, dx = C + \frac{x^{1 + e}}{1 + e}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1  
-----
1 + E

$$\frac{1}{1 + e}$$

  1  
-----
1 + E

$$\frac{1}{1 + e}$$

1/(1 + E)

Numerical answer [src]

0.268941421369995

0.268941421369995

The graph

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