I should have mentioned why I picked that particular sub. If the bracket was just cubed and not to the 3/2, then you could easily multiply it out, divide all the terms by x and integrate term by term. So the u^2 sub gets rid of the fractional exponents and makes life a lot easier.

https://drive.google.com/file/d/1071R2t6LkKuIYGVnfBeD3ho3dz3xMDPM/view?usp=sharingKindly see the solution

I assume that's an "x" in the denominator.

1) Try u^2 = 5x+3. This will get you a rational exp. in u, but the deg(num) > deg(dem)

2) Do a long division and you will a remainder of 18/(u^2-3)

3) Partial fractions on the remainder