> Having just said that, as best as I can tell, taking the derivative
> /usually/ makes something simpler, and taking the integral therefore
> /usually/ makes something more complicated.

Derivatives are easy if you have systematic brain that can follow 
logical methods.  You learn a few simple rules and then you are able to 
pretty much differentiate any function, no matter how complex (it just 
takes up more sheets of paper).

Integration on the other hand requires you to have a different skill, 
one to figure out what function might differentiate to give you back 
your original function.  There are a few common procedures and rules of 
thumb, but faced with an unfamiliar form often requires a bit or trial 
and error or luck...  Luckily at school we had a table of common 
functions and their integral, and I suppose the questions were 
specifically designed to make use of these.  In the real world you seem 
to get stuck very quickly though and just rely on a computer :-)

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