Question

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

Answer 1

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`.