Mister Exam

Other calculators

Solving integrals/ 1/(x*log(x)^3)

Integral of 1/(x*log(x)^3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo             
  /             
 |              
 |      1       
 |  --------- dx
 |       3      
 |  x*log (x)   
 |              
/               
 x              
e
$$\int\limits_{e^{x}}^{\infty} \frac{1}{x \log{\left(x \right)}^{3}}\, dx$$ 
Integral(1/(x*log(x)^3), (x, exp(x), oo))
The answer (Indefinite) [src] 
  /                            
 |                             
 |     1                  1    
 | --------- dx = C - ---------
 |      3                  2   
 | x*log (x)          2*log (x)
 |                             
/
$$\int \frac{1}{x \log{\left(x \right)}^{3}}\, dx = C - \frac{1}{2 \log{\left(x \right)}^{2}}$$
Simplify
The answer [src] 
    1     
----------
     2/ x\
2*log \e /
$$\frac{1}{2 \log{\left(e^{x} \right)}^{2}}$$ 
=
= 
    1     
----------
     2/ x\
2*log \e /
$$\frac{1}{2 \log{\left(e^{x} \right)}^{2}}$$ 
1/(2*log(exp(x))^2)

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

    © Mister Exam – Calculator