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Solving integrals/ 1/(x*(ln^p(x)))

Integral of 1/(x*(ln^p(x))) dx

Limits of integration:

from to
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Piecewise:

The solution

You have entered [src] 
  2             
  /             
 |              
 |      1       
 |  --------- dx
 |       p      
 |  x*log (x)   
 |              
/               
0
$$\int\limits_{0}^{2} \frac{1}{x \log{\left(x \right)}^{p}}\, dx$$ 
Integral(1/(x*log(x)^p), (x, 0, 2))
The answer (Indefinite) [src] 
  /                   //       -log(x)                   \
 |                    ||---------------------  for p != 1|
 |     1              ||     p           p               |
 | --------- dx = C + |<- log (x) + p*log (x)            |
 |      p             ||                                 |
 | x*log (x)          ||     log(log(x))       otherwise |
 |                    \\                                 /
/
$$\int \frac{1}{x \log{\left(x \right)}^{p}}\, dx = C + \begin{cases} - \frac{\log{\left(x \right)}}{p \log{\left(x \right)}^{p} - \log{\left(x \right)}^{p}} & \text{for}\: p \neq 1 \\\log{\left(\log{\left(x \right)} \right)} & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
  2            
  /            
 |             
 |     -p      
 |  log  (x)   
 |  -------- dx
 |     x       
 |             
/              
0
$$\int\limits_{0}^{2} \frac{\log{\left(x \right)}^{- p}}{x}\, dx$$ 
=
= 
  2            
  /            
 |             
 |     -p      
 |  log  (x)   
 |  -------- dx
 |     x       
 |             
/              
0
$$\int\limits_{0}^{2} \frac{\log{\left(x \right)}^{- p}}{x}\, dx$$ 
Integral(log(x)^(-p)/x, (x, 0, 2))

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

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