MathCastle
CalculusMediumNon-Elementary Integration

Non-Elementary Integration · Medium problem

Evaluate the improper integral ∫01dxx(1−x)\displaystyle\int_0^1\dfrac{dx}{\sqrt{x(1-x)}} by recognising it as a Beta function, given Γ ⁣(12)=π\Gamma\!\left(\tfrac12\right)=\sqrt\pi.