# I Was Vey Amaze At The Solution 3

Calculus Level 4

$\cfrac{i\left(\operatorname{Li}_2\left(\cfrac{i+1}{2}\right)-\operatorname{Li}_2\left(i\right)+\operatorname{Li}_2\left(-i\right)-\operatorname{Li}_2\left(-\cfrac{i-1}{2}\right)\right)}{2}$

If the above can be expressed in the form of $$\cfrac{\pi \ln{(q)}}{r}$$, where $$q$$ and $$r$$ are both positive integers and $$q$$ being a prime, find $$q + r$$.

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For more problems like this, try answering this set .

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