Life is complicated. Why does my bank keep sending statements in Spanish, even though I've complained repeatedly that I don't speak Spanish? Where is my digital camera, and why do Canadians buy milk in plastic bags? There is nothing as nice as a solvable, well defined problem. I used to love finding bugs in fake proofs! For your amusement, here's a "proof" for 0=1 :
We start with an innocent looking natural logarithm
Use additivity of integration
And now we substitute y=x/2 in the first, and y=2x in the second integral, which yields
So, we now have ln(2) = 0, divide by ln(2) and voilà :-)
I believe somebody will explain the bug in the comments, so instead of spoiling your fun, I refer you there for debugging.