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Integrate the function (x+3)sqrt(3-4x-...

Integrate the function `(x+3)sqrt(3-4x-x^2)`

Text Solution

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Given,`∫(x+3)√(3-4x-x^2)`
=`-1/2 ∫(-2x-4)√(3-4x-x^2)+ ∫√((√7)^2-(x+2)^2)dx`
`=-1/3 (3-4x-x^2 )^(3/2)+(x+3)/2 √(3-4x-x^2)+7/2 sin^(-1)⁡(x+2)/(√7)+C`
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