Calming

There is nothing more calming that working out few problems. I was looking at this problem that appeared in the recent Pi-Mu journal. Find the int(ln(1+x)/x,x,0,1). One easy way to solve this is using the series of ln(1+x)/x and then you end up with an alternating series which closely resembles bessel problem and then its easy to see that the even terms sum to bessel function. Check the solution here