What is #f(x) = int x-xsec(x/2) dx# if #f((7pi)/4) = 0 #?

1 Answer
Jim H
Nov 23, 2016

Because the indefinite integral involves the imaginary valued polylogarithmic function, I believe that there is an error in the question.

Explanation:

Wolfram Alpha gives the solution to the indefinite integral as

#4i(Li_2(-ie^((ix)/2)) - Li_2(ie^((ix)/2))) +x^2/2-2x(ln(1-ie^((ix)/2)) - ln(1+ie^((ix)/2))) +C#

Now substitute #(7pi)/4# for #x#, set equal to #0# and solve for #C#.

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