It only proves that you cannot rely on calculators and computer algebra systems and internet queries to solve problems for you... and that none of it is a substitute for the human brain.
Im glad you found the right function to use... but had you not thought about it and blindly went along, like most people do, youd be wrong and everything that stems from it would be wrong too. But you shouldnt ever assume that the function you need is built in, or that it is coded correctly, or that you are even using the right function, and you certainly shouldnt take it on blind faith.
In my humble opinion, a mathematician that cannot do on paper what a computer does for him, is not mathematician at all. Using the tool is one thing, relying on it is quite another, especially if you dont understand what is going on behind the scenes.