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Solving integrals/ dx/ln^5x

Integral of dx/ln^5x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo           
  /           
 |            
 |     1      
 |  ------- dx
 |     5      
 |  log (x)   
 |            
/             
2
$$\int\limits_{2}^{\infty} \frac{1}{\log{\left(x \right)}^{5}}\, dx$$ 
Integral(1/(log(x)^5), (x, 2, oo))
The answer (Indefinite) [src] 
  /                                                                  
 |                                      2           3                
 |    1             li(x)   -6*x - x*log (x) - x*log (x) - 2*x*log(x)
 | ------- dx = C + ----- + -----------------------------------------
 |    5               24                          4                  
 | log (x)                                  24*log (x)               
 |                                                                   
/
$$\int \frac{1}{\log{\left(x \right)}^{5}}\, dx = C + \frac{- x \log{\left(x \right)}^{3} - x \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} - 6 x}{24 \log{\left(x \right)}^{4}} + \frac{\operatorname{li}{\left(x \right)}}{24}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     li(2)
oo - -----
       24
$$- \frac{\operatorname{li}{\left(2 \right)}}{24} + \infty$$ 
=
= 
     li(2)
oo - -----
       24
$$- \frac{\operatorname{li}{\left(2 \right)}}{24} + \infty$$ 
oo - li(2)/24

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

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