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Math Help - Series/Taylor

  1. #1
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    Series/Taylor

    Evaluate the integral as a power series. What is the radius of convergence?

    1) integral of [ ln(1-t) / t ] dt

    Evaluate the indefinite integral as an infinite series

    2) integral of [(e^x-1)/x ]dx

    Can someone show me how these are done? thank you
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  2. #2
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    Quote Originally Posted by xfyz View Post

    2) integral of [(e^x-1)/x ]dx

    Can someone show me how these are done? thank you
    e^x = 1+x+x^2/2!+x^3/3!+...
    So,
    e^x - 1 = x+x^2/2!+x^3/3!+...
    Thus,
    (e^x-1)/x = 1 + x/2!+x^2/3!+...
    Now integrate term-by-term and what do you get?
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    e^x = 1+x+x^2/2!+x^3/3!+...
    So,
    e^x - 1 = x+x^2/2!+x^3/3!+...
    Thus,
    (e^x-1)/x = 1 + x/2!+x^2/3!+...
    Now integrate term-by-term and what do you get?
    After I integrate each term, am i done? This is where i get confused in this whole series topic. After i am finished integrating that

    x + x^2 / 2*2! + x^4 / 4*3! + ... am i done?
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  4. #4
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    Quote Originally Posted by xfyz View Post
    After I integrate each term, am i done?
    Yes there is no other way to integrate this function. The answer that you got is the anti-derivative just in infinite series form.
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