Let ∫x√1+x−x2 dx=α(1+x−x2)3/2+β[(x−12)√1+x−x2+γsin− – InterviewSolution

1.	Let ∫x√1+x−x2 dx=α(1+x−x2)3/2+β[(x−12)√1+x−x2+γsin−12x−1√5]+C (where α,β,γ are constants). Then the value of 3(β−γα) is(where C is integration constant)
Answer» Let $\int x \sqrt{1 + x - x^{2}} d x = α (1 + x - x^{2})^{3 / 2} + β [(x - \frac{1}{2}) \sqrt{1 + x - x^{2}} + γ {sin}^{- 1} \frac{2 x - 1}{\sqrt{5}}] + C$ (where $α, β, γ$ are constants). Then the value of $3 (\frac{β - γ}{α})$ is $($ where $C$ is integration constant $)$

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