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Solving integrals/ x^(n-1)

Integral of x^(n-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |   n - 1   
 |  x      dx
 |           
/            
0
$$\int\limits_{0}^{1} x^{n - 1}\, dx$$ 
Integral(x^(n - 1), (x, 0, 1))
Detail solution

  1. The integral of is when :

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                //   n                   \
 |                 ||  x                    |
 |  n - 1          ||  --    for n - 1 != -1|
 | x      dx = C + |<  n                    |
 |                 ||                       |
/                  ||log(x)     otherwise   |
                   \\                       /
$$\int x^{n - 1}\, dx = C + \begin{cases} \frac{x^{n}}{n} & \text{for}\: n - 1 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
/     n                                  
|1   0                                   
|- - --  for And(n > -oo, n < oo, n != 0)
$$\begin{cases} - \frac{0^{n}}{n} + \frac{1}{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\infty & \text{otherwise} \end{cases}$$ 
=
= 
/     n                                  
|1   0                                   
|- - --  for And(n > -oo, n < oo, n != 0)
$$\begin{cases} - \frac{0^{n}}{n} + \frac{1}{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\infty & \text{otherwise} \end{cases}$$ 
Piecewise((1/n - 0^n/n, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (oo, True))

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

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