I am wondering if any problems have been designed that test a wide range of mathematical skills. For example, I remember doing the integral $$\int \sqrt{\tan x}\;\mathrm{d}x$$ and being impressed at how many techniques (substitution, trig, partial fractions etc.) I had to use to solve it successfully.
I am looking for suggestions/contributions to help build up such a question. For example, one problem could have as its answer $\tan x$ which would then be used in the integral, and something about the answer to the integral could lead into the next part.
The relevant subjects would be anything covered in the first few years of an undergraduate degree in mathematics.
The main reason I ask is that I want to work on developing some more integrated ways to practice mathematics "holistically" which I feel is very lacking in the current educational model.
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