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-1/(y*log(y))
Solving integrals/ -1/(y*log(y))

Integral of -1/(y*log(y)) dy

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1            
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 |    -1       
 |  -------- dy
 |  y*log(y)   
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0
∫01(−1ylog⁡(y)) dy\int\limits_{0}^{1} \left(- \frac{1}{y \log{\left(y \right)}}\right)\, dy 
Integral(-1/(y*log(y)), (y, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫(−1ylog⁡(y)) dy=−∫1ylog⁡(y) dy\int \left(- \frac{1}{y \log{\left(y \right)}}\right)\, dy = - \int \frac{1}{y \log{\left(y \right)}}\, dy

    1. Don't know the steps in finding this integral.

      But the integral is

      log⁡(log⁡(y))\log{\left(\log{\left(y \right)} \right)}

    So, the result is: −log⁡(log⁡(y))- \log{\left(\log{\left(y \right)} \right)}

  2. Add the constant of integration:

    −log⁡(log⁡(y))+constant- \log{\left(\log{\left(y \right)} \right)}+ \mathrm{constant}

The answer is:

−log⁡(log⁡(y))+constant- \log{\left(\log{\left(y \right)} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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 |   -1                         
 | -------- dy = C - log(log(y))
 | y*log(y)                     
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∫(−1ylog⁡(y)) dy=C−log⁡(log⁡(y))\int \left(- \frac{1}{y \log{\left(y \right)}}\right)\, dy = C - \log{\left(\log{\left(y \right)} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010000
Plot the graph f(x)
The answer [src] 
oo
∞\infty 
=
= 
oo
∞\infty 
oo
Numerical answer [src] 
47.8772101199067
47.8772101199067
The graph
Integral of -1/(y*log(y)) dy

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

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