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Math Help - Definite integral substitution???

  1. #1
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    Definite integral substitution???

    Hi all,

    I am struggling to find a way to substitution for integral of x^2/sqr(1-x)dx.
    If it was x^3 in the square root I would know how to do it, but because numerator is lower power than denominator

    Thanks
    alex
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by rexexdesign View Post
    Hi all,

    I am struggling to find a way to substitution for integral of x^2/sqr(1-x)dx.
    If it was x^3 in the square root I would know how to do it, but because numerator is lower power than denominator

    Thanks
    alex
    \int\frac{x^2}{\sqrt{1-x}}dx

    let u=\sqrt{1-x}\Rightarrow{x=1-u^2}

    So dx=-2udu

    and x^2=(1-u^2)^2

    So now we have

    \int\frac{-2u(1-u^2)^2}{u}du

    I think you can take it from there
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  3. #3
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    You are right. My teacher did not teach us that before. She always said find the outside and inside function and make substitutions, like \sqrt{x-1}\ would be f(x)=\sqrt{x}\ and g(x)=x-1

    thanks for the tip.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by rexexdesign View Post
    You are right. My teacher did not teach us that before. She always said find the outside and inside function and make substitutions, like \sqrt{x-1}\ would be f(x)=\sqrt{x}\ and g(x)=x-1

    thanks for the tip.
    It is an art form though. As I am sure most will attest on this website it takes a while to see whether you should for this example

    Let u=\sqrt{1-x}

    or Let u=1-x
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