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

1 Answer
Jim H
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.

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