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

1 Answer
Mar 22, 2016

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.