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\[ \int \sqrt{\dfrac{1-\sqrt{x}}{1+\sqrt{x}}} \, dx = \ ? \]

How many positive integer solutions \((a, b)\) does the equation \[ a^2+b^2+(a+b)^2=b^3\] have, where \(0<b<2017?\)

The solution of \(\dfrac { dy }{ dx } =\dfrac { { x }^{ 2 }+{ y }^{ 2 }+1 }{ 2xy } \) satisfying \(y(1)=0\) is given by

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\(p, q,\) and \((p^q+q^p)\) are all prime numbers. What is the largest possible sum of the three numbers: \[p+q+(p^q+q^p) ?\]

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