# Thread: [SOLVED] Easy Integration by Substitution

1. ## [SOLVED] Easy Integration by Substitution

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