# Integral of an Irrational Function

Calculus Level 5

$\text{I} = \int_{0}^{1} \dfrac{\sqrt{x}\sqrt{1-x}}{(1+x)(x^2+1)} \mathrm{d}x$

If $$\text{I}$$ can be expressed as $$\displaystyle \dfrac {{\pi}^{A}}{\sqrt {2}} \left(\sqrt{\sqrt{\text{B}}} \cos\left(\dfrac{\text{C}\pi}{\text{D}}\right) - \text{E} \right)$$ where $$\text{A},\text{B},\text{C},\text{D}$$ and $$\text{E}$$ are positive integers, $$\gcd (\text{C},\text{D}) =1$$ and $$\text{B}$$ is a prime number.

Evaluate $$\text{A}+\text{B}+\text{C}+\text{D}+\text{E}$$

×