A neat integral
First post 🎉
The problem
A friend (who loves his integrals very dearly) found this interesting one to work on. One substitution later, we were left with this seemingly impossible integrand.
However, with the clever use of Maclaurin series, we were able to reduce it to the sum of reciprocal of squares (aka the Basel problem), which is a well known result.
Our full solution is surprisingly short.
What's more, π seemingly appears out of nowhere when we are only dealing with exponentials and logarithms! Pretty neat huh.
What's more surprising is that my first post is about an integral rather than number theory -gasp
...Safe to say not much revision has been done during that maths class today :)