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Integrate the functionssqrt(x^2+3x)...

Integrate the functions`sqrt(x^2+3x)`

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`" Let " I= int sqrt(x^(2)+3x) dx`
`=int sqrt(x^(2)+3x+((3)/(2))^(2)-((3)/(2))^(2))dx`
`=int sqrt((x+(3)/(2))^(2)-((3)/(2))^(2))dx`
`=(x+(3)/(2))/(2)sqrt((x+(3)/(2))^(2)-((3)/(2))^(2))`
`-(9)/(4xx2)log|(x+(3)/(2))+sqrt(x^(2)+3x)|+C`
`rArr I=(2x+3)/(4)sqrt(x^(2)+3x)`
`-(9)/(8)log|((2x+3)/(2))+sqrt(x^(2)+3x)|+C`
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