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

1 Answer
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.