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 $$A+B+C+D$$

×