A calculus problem by Kishore S Shenoy

Calculus Level 5

\[\int_0^{100}\int_0^{\pi/2} \dfrac{\ln\left(1+x\sin^2\theta\right)}{\sin^2\theta}\, d\theta\, dx\]

If the above integral can be written as \(\dfrac {A\pi} B\left(C\sqrt C-D\right)\), where \(A\), \(B\), \(C\) and \(D\) are natural numbers with least values, find \(A+B+C+D\)

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