How do I evaluate #int3 sin(ln(x))dx#?
The answer is
This integral has to be done two times by parts because it is a cyclic integral. A cyclic integral is an integral of a cyclic function, like
The theorem of integration by parts says:
In this case, it seems that there is only one function, but it is not true because we can assume that
For the first step it is necessary to find
Now it is necessary to make another time the integration by parts:
because the last integral is identical to the first.