Don`t need to do math, just tell me where i screwed up?

I have the question: Integral of (x^2)/(1-x)^.5

I need to find the indefinete integral

However the answer I got was different from the correct one. I will briefly list my method below:

Let u = 1-x therefore x=1-u, sub into original equation,

this leaves du = -dx or -du=dx sub into original equation

I then expand the numerator (which is now (1-u)^2) and get the equation

integral of (1-2u+u^2)/u^.5 all times du

note:forgot all this is *-1 from dx=-du, however my answer is off by more than a factor of -1

Since each term 1, 2u, u^2 is separated by addition/subtraction I treat each like its own integral and proceed to remove the denominator getting:

integral of u^-.5( aka 1/u^.5) - integral of 2u^.5 + integral of u^1.5

Antideriving these and subbing u=1-x for all of them yields a rough answer of

2(1-x)^.5 - (4/3)*(1-x)^3/2 + (2/5)*(1-x)^5/2 + C

However the correct answer is

(1-x)^.5 * (6x^2+8x+16)/15 I understand they factored some things out and simplified but after simplifiying i was not close at all

Please help, I have absolutely no idea what i did wrong, you don't need to solve it (I'd actually like to attempt it myself once I figure out what i did wrong), just need to know what I did wrong

Ha i figured it out, I really guess I can't do basic arithmatic. After factoring out the sqrt(1-x) it leaves easily divisible exponents which cancel (for the most part) and allow me to simplify, thanks anyway guys, i'm sure i'll be back before my calc class is done haha