`sqrt(x^(2)+3x)`

Explanation

माना `I=intsqrt(x^(2)+3xdx`
`=intsqrt(x^(2)+3x+((3)/(2))^(2)-((3)/(2))^(2))dx`
`=intsqrt((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`