$\displaystyle \int(\ln(x))^2dx$
First one to get this really easy integral wins....uhm.....wins...my admiration!
Who is the fastest typer?
If I said something like
$\displaystyle \int \left ( ln(x) \right ) ^2~dx = \int \left ( (x - 1)^2 - (x - 1)^3 + \frac{11(x - 1)^4)}{12} - \frac{5(x - 1)^5}{6} + ~...~ \right ) ~dx$
$\displaystyle = \frac{15}{4}x - \frac{77}{12}x^2 + \frac{107}{18}x^3 - \frac{13}{4}x^4 + \frac{61}{60}x^5 - \frac{5}{36}x^6 + ~...$
you'd probably get mad at me, wouldn't you?
-Dan