How do I evaluate #int3 sin(ln(x))dx#?
1 Answer
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
So:
Now it is necessary to make another time the integration by parts:
So:
because the last integral is identical to the first.
So: