# A calculus problem by Kishore S Shenoy

Calculus Level 5

$\large \int_0^{\pi/4}\dfrac{\sec x}{1+2\sin^2 x}\,dx$

If the value of the above integral can be written as $$\dfrac{\sqrt A}B\pi^C + \dfrac1 B\ln\left(D+B\sqrt A\right)$$, where $$A,B,C$$ and $$D$$ are positive integers with minimised $$A$$, find $$A+2B+C+D$$.

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