# What substitution should I make?

Calculus Level 5

$\large \int_{0}^{1}\sqrt{x+\sqrt{x^2+1}} \, dx=\dfrac AB \left(1 + \sqrt{\sqrt C - D} \right)$

If the equation above holds true for positive integers $$A,B, C$$ and $$D$$ such that $$A$$ and $$B$$ are coprime, find the value of $$A+B+C+D$$.

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