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Math Help - [SOLVED] Easy Integration by Substitution

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    [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

    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
    Last edited by someguy456345; April 13th 2009 at 06:10 PM. Reason: realised i forgot -1 from dx=-du
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