I think that I must be the stupidest person alive but I can not get this.
I get sin(x)(-cos(x) - integral of (-cos(x) times cos(x) dx
which goes to sin(x)(-cos(x) + integral of cos^2(x) dx
and now I have the same type of problem all over again and I do not see how using by parts will be anything but an endless loop!!! I know I am missing the point but I feel helpless and hopeless to figure out why. Can anyone explain it to me?????