Integral involving Elliptic Integral
Calculus
Level
5
The following integral evaluates to:
\[\int_0^1 \left(E(k)-\dfrac{\pi}{2}\right)\,\frac{dk}{k}=a+\dfrac{\pi}{b}+c\int_0^{\pi/4} \ln(\cos x)\,dx\]
where \(a\), \(b\) and \(c\) are integers. Find \(|a|+|b|+|c|\).
Details and Assumptions:
- \(E(k)\) is complete elliptic integral of the second kind.
by
Pranav Arora