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Solving integrals/ x/ln(x)

Integral of x/ln(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
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 |    x      
 |  ------ dx
 |  log(x)   
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0
∫01xlog⁡(x) dx\int\limits_{0}^{1} \frac{x}{\log{\left(x \right)}}\, dx 
Integral(x/log(x), (x, 0, 1))
Detail solution

  1. Let u=log⁡(x)u = \log{\left(x \right)}.

    Then let du=dxxdu = \frac{dx}{x} and substitute dudu:

    ∫e2uu du\int \frac{e^{2 u}}{u}\, du

      EiRule(a=2, b=0, context=exp(2*_u)/_u, symbol=_u)

    Now substitute uu back in:

    Ei⁡(2log⁡(x))\operatorname{Ei}{\left(2 \log{\left(x \right)} \right)}

  2. Add the constant of integration:

    Ei⁡(2log⁡(x))+constant\operatorname{Ei}{\left(2 \log{\left(x \right)} \right)}+ \mathrm{constant}

The answer is:

Ei⁡(2log⁡(x))+constant\operatorname{Ei}{\left(2 \log{\left(x \right)} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
 |                             
 |   x                         
 | ------ dx = C + Ei(2*log(x))
 | log(x)                      
 |                             
/
∫xlog⁡(x) dx=C+Ei⁡(2log⁡(x))\int \frac{x}{\log{\left(x \right)}}\, dx = C + \operatorname{Ei}{\left(2 \log{\left(x \right)} \right)}
Simplify
The answer [src] 
-oo
−∞-\infty 
=
= 
-oo
−∞-\infty 
-oo
Numerical answer [src] 
-42.820593940758
-42.820593940758

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

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