Question by bloodninja: Where can I find challenging calculus problems?
I am interested in some challenging calc problems that require some creativity to solve, a stretching of the mind, something like that. Perhaps an insight or two here and there. Such problems were far and few in my Calc I textbook and as I independently study Calc II I am also not finding many of those. The study of calculus has so far been much fun than the study of algebra where one could easily find hundreds of challenging problems on the internet.

Best answer:

Answer by Mαtt
integrate

sq rt(tan(x))

Here are some hints:
it requires 6 separate uses of u-substitution and two separate uses of partial fractions expansion. I’ll be happy to send you the solution if you want.

Calculus isn’t that interesting until you take vector calculus, then you start to see a lot of ideas come together.

Find the area under the curve
1/(2 + cos(x))
from 0 ≤ x ≤ π/2

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