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Integral of nx^(n-1) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |     n - 1   
 |  n*x      dx
 |             
/              
0              
$$\int\limits_{0}^{1} n x^{n - 1}\, dx$$
Integral(n*x^(n - 1), (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. The integral of is when :

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

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

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