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  • Identical expressions

  • (d*x)/(x*ln^ five *x)
  • (d multiply by x) divide by (x multiply by ln to the power of 5 multiply by x)
  • (d multiply by x) divide by (x multiply by ln to the power of five multiply by x)
  • (d*x)/(x*ln5*x)
  • d*x/x*ln5*x
  • (d*x)/(x*ln⁵*x)
  • (dx)/(xln^5x)
  • (dx)/(xln5x)
  • dx/xln5x
  • dx/xln^5x
  • (d*x) divide by (x*ln^5*x)
  • (d*x)/(x*ln^5*x)dx
Solving integrals/ (d*x)/(x*ln^5*x)

Integral of (d*x)/(x*ln^5*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo             
  /             
 |              
 |     d*x      
 |  --------- dx
 |       5      
 |  x*log (x)   
 |              
/               
E
∫e∞dxxlog⁡(x)5 dx\int\limits_{e}^{\infty} \frac{d x}{x \log{\left(x \right)}^{5}}\, dx 
Integral((d*x)/((x*log(x)^5)), (x, E, oo))
The answer (Indefinite) [src] 
  /                                                                              
 |                                              2             3                  
 |    d*x             d*li(x)   -6*d*x - d*x*log (x) - d*x*log (x) - 2*d*x*log(x)
 | --------- dx = C + ------- + -------------------------------------------------
 |      5                24                               4                      
 | x*log (x)                                        24*log (x)                   
 |                                                                               
/
∫dxxlog⁡(x)5 dx=C+dli⁡(x)24+−dxlog⁡(x)3−dxlog⁡(x)2−2dxlog⁡(x)−6dx24log⁡(x)4\int \frac{d x}{x \log{\left(x \right)}^{5}}\, dx = C + \frac{d \operatorname{li}{\left(x \right)}}{24} + \frac{- d x \log{\left(x \right)}^{3} - d x \log{\left(x \right)}^{2} - 2 d x \log{\left(x \right)} - 6 d x}{24 \log{\left(x \right)}^{4}}
Simplify
The answer [src] 
             d*li(E)   5*E*d
oo*sign(d) - ------- + -----
                24       12
−dli⁡(e)24+5ed12+∞sign⁡(d)- \frac{d \operatorname{li}{\left(e \right)}}{24} + \frac{5 e d}{12} + \infty \operatorname{sign}{\left(d \right)} 
=
= 
             d*li(E)   5*E*d
oo*sign(d) - ------- + -----
                24       12
−dli⁡(e)24+5ed12+∞sign⁡(d)- \frac{d \operatorname{li}{\left(e \right)}}{24} + \frac{5 e d}{12} + \infty \operatorname{sign}{\left(d \right)} 
oo*sign(d) - d*li(E)/24 + 5*E*d/12

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

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