Integral of y/lny dx

The solution

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  1          
  /          
 |           
 |    y      
 |  ------ dy
 |  log(y)   
 |           
/            
0

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

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

Detail solution

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

Then let $du = \frac{dy}{y}$ and substitute $du$ :

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                            
 |                             
 |   y                         
 | ------ dy = C + Ei(2*log(y))
 | log(y)                      
 |                             
/

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

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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Identical expressions

Integral of y/lny dx

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The solution