Before I started teaching A-Level I hadn’t done an integral by hand for about 5 years – I would always use Mathematica when I had to evaluate an integral symbolically.
I’ve actually enjoyed re-familiarising myself with some of the techniques required for some of the more difficult integrands and fancied looking at some more challenging integrals and so I bought the book “Inside Interesting Integrals” by Paul J. Nahin. This is a great book packed full of clever tricks to evaluate integrals and I thought as it is the last day of the holidays (and so don’t want to write a long post) I would share one of them here.
Hence, the original definite integral is equal to \(\pi / 4 \). I think this is pretty neat!