If ∫dxx2-4x=-122fx+142logx-2x+2+C where C is constant of integration and f2=π4 and f6+f23 is equal to

Question

\int \frac{dx}{(x^{2} - 4) \sqrt{x}} = - \frac{1}{2 \sqrt{2}} f (x) + \frac{1}{4 \sqrt{2}} \log |\frac{\sqrt{x} - \sqrt{2}}{\sqrt{x} + \sqrt{2}}| + C

where

C

is constant of integration and

f (2) = \frac{π}{4}

and

f (6) + f (\frac{2}{3})

is equal to

\frac{π}{4}

\frac{π}{2}

\frac{3 π}{2}

- \frac{π}{4}

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