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

Integral of -1/(x*log(x)) dx

Limits of integration:

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Piecewise:

The solution

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

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

    ∫(−1xlog⁡(x)) dx=−∫1xlog⁡(x) dx\int \left(- \frac{1}{x \log{\left(x \right)}}\right)\, dx = - \int \frac{1}{x \log{\left(x \right)}}\, dx

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

      But the integral is

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

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

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                             
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 |   -1                         
 | -------- dx = C - log(log(x))
 | x*log(x)                     
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∫(−1xlog⁡(x)) dx=C−log⁡(log⁡(x))\int \left(- \frac{1}{x \log{\left(x \right)}}\right)\, dx = C - \log{\left(\log{\left(x \right)} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90020000
Plot the graph f(x)
The answer [src] 
oo
∞\infty 
=
= 
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∞\infty 
oo
Numerical answer [src] 
47.8772101199067
47.8772101199067
The graph
Integral of -1/(x*log(x)) dx

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

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