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Solving integrals/ 1/n^x

Integral of 1/n^x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1      
  /      
 |       
 |  1    
 |  -- dx
 |   x   
 |  n    
 |       
/        
0
$$\int\limits_{0}^{1} \frac{1}{n^{x}}\, dx$$ 
Integral(1/(n^x), (x, 0, 1))
The answer (Indefinite) [src] 
  /            //  -x                   \
 |             ||-n                     |
 | 1           ||------  for log(n) != 0|
 | -- dx = C + |
$$\int \frac{1}{n^{x}}\, dx = C + \begin{cases} - \frac{n^{- x}}{\log{\left(n \right)}} & \text{for}\: \log{\left(n \right)} \neq 0 \\x & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
/  1         1                                       
|------ - --------  for Or(And(n >= 0, n < 1), n > 1)
$$\begin{cases} \frac{1}{\log{\left(n \right)}} - \frac{1}{n \log{\left(n \right)}} & \text{for}\: \left(n \geq 0 \wedge n < 1\right) \vee n > 1 \\1 & \text{otherwise} \end{cases}$$ 
=
= 
/  1         1                                       
|------ - --------  for Or(And(n >= 0, n < 1), n > 1)
$$\begin{cases} \frac{1}{\log{\left(n \right)}} - \frac{1}{n \log{\left(n \right)}} & \text{for}\: \left(n \geq 0 \wedge n < 1\right) \vee n > 1 \\1 & \text{otherwise} \end{cases}$$ 
Piecewise((1/log(n) - 1/(n*log(n)), (n > 1)∨((n >= 0)∧(n < 1))), (1, True))

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

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