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Evaluate: int(2x-5)sqrt(2+3x-x^2)dx...

Evaluate: `int(2x-5)sqrt(2+3x-x^2)dx`

Text Solution

Verified by Experts

Let `I =int(2 x-5) sqrt{2+3 x-x^{2}} {dx} `
`2 x-5=lambda frac{d}{d x}(2+3 x-x^{2})+mu `
`Rightarrow 2 x-5=lambda(-2 x+3)+mu `
`Rightarrow 2 x-5=(-2 lambda) x+3 lambda+mu`
Equating coeffieicents
`-2 lambda=2 `
`Rightarrow lambda=-1`
`3 lambda+mu=-5 `
...
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