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Math Help - power series representation

  1. #1
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    power series representation

    find the power series representation.

    heres the equation: http://img260.imageshack.us/img260/7458/untitledfl9.jpg


    i'm horrible with integration. can someone provide me some steps please.
    appreciate any help.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    find the power series representation.

    heres the equation: http://img260.imageshack.us/img260/7458/untitledfl9.jpg


    i'm horrible with integration. can someone provide me some steps please.
    appreciate any help.
    The idea where is that function is not integratable.
    -\frac{ \ln (1-t)}{t} .
    But we know that, for |t|<-1
    \ln (1-t)=-t-\frac{t^2}{2}-\frac{t^3}{3}-...
    Let us make the resistriction 0<t<1.
    Then,
    -\frac{\ln(1-t)}{t}=1+\frac{t}{2}+\frac{t^2}{3}+...
    Then if you integrate this,
    x+\frac{x^2}{2^2}+\frac{x^3}{3^2}+...
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