Indefinite Integrals

Try multiply top and bottom by sqrt(x+3)-sqrt(x) to turn the expression to:

( sqrt(x+3)-sqrt(x) ) / (x+3-x)
=( sqrt(x+3)-sqrt(x) ) / 3
=sqrt(x+3)/3 -sqrt(x)/3

Each of the two terms can be integrated by elementary forms, giving

I=(2/9) ( (x+3)^(3/2) - x^(3/2) )

anw=dx