Integral
Integral from 0 to 1 of ln(x+1)/(x^2 +1) dx isn't that hard actually but I only know one way to do it.
1/(x^2+1) = (arctg x)' ... (ie the derivate of arctan x) tg(x)=tan(x)
you change the variable and the integral becomes
integral from 0 to pi/4 of ln(1+tg(x)) dx
by making the...