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Solving integrals/ x^e

Integral of x^e dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1      
  /      
 |       
 |   E   
 |  x  dx
 |       
/        
0
∫01xe dx\int\limits_{0}^{1} x^{e}\, dx 
Integral(x^E, (x, 0, 1))
Detail solution

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

    ∫xe dx=x1+e1+e\int x^{e}\, dx = \frac{x^{1 + e}}{1 + e}

  2. Add the constant of integration:

    x1+e1+e+constant\frac{x^{1 + e}}{1 + e}+ \mathrm{constant}

The answer is:

x1+e1+e+constant\frac{x^{1 + e}}{1 + e}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |              1 + E
 |  E          x     
 | x  dx = C + ------
 |             1 + E 
/
∫xe dx=C+x1+e1+e\int x^{e}\, dx = C + \frac{x^{1 + e}}{1 + e}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
  1  
-----
1 + E
11+e\frac{1}{1 + e} 
=
= 
  1  
-----
1 + E
11+e\frac{1}{1 + e} 
1/(1 + E)
Numerical answer [src] 
0.268941421369995
0.268941421369995
The graph
Integral of x^e dx

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

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