Mister Exam

Integral of ln(lnx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1               
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 |  log(log(x)) dx
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$$\int\limits_{0}^{1} \log{\left(\log{\left(x \right)} \right)}\, dx$$
Integral(log(log(x)), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. There are multiple ways to do this integral.

      Method #1

      1. Let .

        Then let and substitute :

        1. Use integration by parts:

          Let and let .

          Then .

          To find :

          1. Let .

            Then let and substitute :

            1. The integral of the exponential function is itself.

            Now substitute back in:

          Now evaluate the sub-integral.

        2. Let .

          Then let and substitute :

            EiRule(a=1, b=0, context=exp(_u)/_u, symbol=_u)

          Now substitute back in:

        Now substitute back in:

      Method #2

      1. Use integration by parts:

        Let and let .

        Then .

        To find :

        1. The integral of the exponential function is itself.

        Now evaluate the sub-integral.

        EiRule(a=1, b=0, context=exp(_u)/_u, symbol=_u)

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                               
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 | log(log(x)) dx = C - Ei(log(x)) + x*log(log(x))
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$$\int \log{\left(\log{\left(x \right)} \right)}\, dx = C + x \log{\left(\log{\left(x \right)} \right)} - \operatorname{Ei}{\left(\log{\left(x \right)} \right)}$$
The graph
The answer [src]
-EulerGamma
$$- \gamma$$
=
=
-EulerGamma
$$- \gamma$$
-EulerGamma
Numerical answer [src]
(-0.577215664901533 + 3.14159265358979j)
(-0.577215664901533 + 3.14159265358979j)
The graph
Integral of ln(lnx) dx

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