Question

How would you integrate

18x-33/√(3x^2-11x+6)

Answer 1

I assume you meant:

(18x-33)/√(3x^2-11x+6)
or
(18x-33)/(3x^2-11x+6)^(-1/2)

did you notice that 18x-33 is 3 times the derivative of 3x^2 - 11x + 6 ?

so by just plain common intuition ....

6(3x^2 - 11x + 6)^(1/2) + c
or
6√(3x^2 - 11x + 6) + c

(check by taking the derivative, it works)