Integral of x/lnx dx

The solution

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  1          
  /          
 |           
 |    x      
 |  ------ dx
 |  log(x)   
 |           
/            
0

$$\int\limits_{0}^{1} \frac{x}{\log{\left(x \right)}}\, dx$$

Integral(x/log(x), (x, 0, 1))

Detail solution

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

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

$\int \frac{e^{2 u}}{u}\, du$
Now substitute $u$ back in:

$\operatorname{Ei}{\left(2 \log{\left(x \right)} \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                            
 |                             
 |   x                         
 | ------ dx = C + Ei(2*log(x))
 | log(x)                      
 |                             
/

$$\int \frac{x}{\log{\left(x \right)}}\, dx = C + \operatorname{Ei}{\left(2 \log{\left(x \right)} \right)}$$

Simplify

The answer [src]

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$$-\infty$$

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$$-\infty$$

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Numerical answer [src]

-42.820593940758

-42.820593940758

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

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Integral of x/lnx dx

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