6). (x^3 + 3x^2 - 9) / (x + 3)^1/2 dx

Consider:

Now let t2 = x + 3 then 2tdt = dx and x - t2 - 3.

But t2 = x + 3

Again consider:

Take u2 = x + 3 then 2udu = dx

But u2 = x + 3

Therefore