# Remembering a friend: Azhaghu Roopesh M

Calculus Level 5

For $$|a|>\dfrac{1}{2}$$, $\int \dfrac{dx}{(\sin x + a \sec x)^2} =$ $\dfrac{1}{\alpha a^2 - 1}\times \dfrac{\cos 2x}{\beta a +\sin 2x} + \dfrac{4a}{(\alpha a^2-1)^{\frac{3}{2}}}tan^{-1} \left(\dfrac{2a \tan x +1}{\sqrt{\alpha a^2-1}}\right) - \dfrac{1}{\beta a+\sin 2x} + C$If $$p+q+r=0$$ and $$p^2+q^2+r^2 = \alpha-\beta-1$$, then the maximum value of$p^{333}+q^{333}+r^{333}$ is equal to $$\dfrac{j^k - j}{l^m\sqrt{l}}$$. Find $$j+k+l+m$$.

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