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I stumbled upon an apparently time-exhaustive question and I wanted to check whether there was an effective method for the following problem; if yes, please help me out!

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1. Let $F_n(x)= \left( f_1 \circ f_2 \circ \ldots \circ f_n \right) (x)$. What kinds of composition satisfy $\forall x, F_n(-x)=-F_n(x)$(‘odd function’) where $f_i(x) (i=1,2, \ldots, n)$ is not an …

I have listed challenging calculus problems. These are all my original problems except 4.

Note1: 1. and 3. are very challenging.

Note2: 4. 6. are related.

Note3: Most of them …

The problem

A uniform disc of radius $R$ rests with one of its flat faces on a horizontal floor. Coefficient of friction between the disc and the floor is ...

What kind(s) of substitution is(are) involved in this monstrous integral?

$\int\frac{x}{\sqrt{x^4+10x^2-96x-71}} \, dx = -\frac18 \ln((x^6+15x^4-80x^3+27x^2-528x+781)\sqrt{x^4+10x^2-96x-71}-(x^8+20x^6-128x^5+54x^4-1408x^3+3124x^2+10001))+constant$

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