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Evaluate: int(3x+1)/(sqrt(5-2x-x^2))dx...

Evaluate: `int(3x+1)/(sqrt(5-2x-x^2))dx`

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I=`int(3x+1)/(sqrt(5-2x-x^2))dx`
Rewrite numerator `(3x+1)as=3/2​(−2x−2+4/3​)`
⟹`−3/2​∫(​−2x−2)/(sqrt(5−2x−x^2 ))dx​-2∫dx/sqrt(5−2x−x^2) `
For first integral Let `5−2x−x^2=t⟹(−2−2x)dx=dt `
⟹`−3/2​∫(dt)/(sqrt(t ))dx​-2∫dx/sqrt(6-(x+1)^2) ...
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