Question

What is `f(x) = int secx-xtanx dx` if `f((5pi)/3) = 0`?

Answer 1

`int(secx-xtanx)dx = -1/2iLi_2(-e^(2ix))-(ix^2)/2+xln(1+e^(2ix))-ln(cos(x/2)-sin(x/2))+ln(sin(x/2)+cos(x/2))+C` (where `Li_n(x)` is the polylogarithmic function).

Explanation:

Now simply plug in the `(5pi)/3`, set the result equal to `0` and solve to get `C = -1-isqrt3+(35ipi^2)/18+ln2-2ln(sqrt3-1)`.

I suspect that the question is mis-typed.