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The following integral evaluates to:
∫01(E(k)−π2) dkk=a+πb+c∫0π/4ln(cosx) dx\int_0^1 \left(E(k)-\dfrac{\pi}{2}\right)\,\frac{dk}{k}=a+\dfrac{\pi}{b}+c\int_0^{\pi/4} \ln(\cos x)\,dx∫01(E(k)−2π)kdk=a+bπ+c∫0π/4ln(cosx)dx
where aaa, bbb and ccc are integers. Find ∣a∣+∣b∣+∣c∣|a|+|b|+|c|∣a∣+∣b∣+∣c∣.
Details and Assumptions:
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