Evaluate `intsqrt(x^(2)+3x)dx`.

Explanation

We have `(x^(2)+3x)={x^(2)+3x+((3)/(2))^(2)-((3)/(2))^(2)}=(x+(3)/(2))^(2)-((3)/(2))^(2)`.
`thereforeI=intsqrt(x^(2)+3x)dx`
`=intsqrt((x+(3)/(2))^(2)-((3)/(2))^(2))dx=intsqrt(t^(2)-((3)/(2))^(2))dt "where"(x+(3)/(2))=t`
`=(1)/(2)tsqrt(t^(2)-(9)/(4))-(9)/(8)log|t+sqrt(t^(2)-(9)/(4))|+C`
`{"using"intsqrt(x^(2)-a^(2))dx=(x)/(2)sqrt(x^(2)-a^(2))-(a^(2))/(2)log|x+sqrt(x^(2)-a^(2))|+C}`
`=(1)/(2)(x(3)/(2))sqrt(x^(2)+3x)-(9)/(8)log|(x+(3)/(2))+sqrt(x^(2)+3x)|+C`.