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Math Help - Improper Integral Problem

  1. #1
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    Improper Integral Problem

    if k>0 ,show that \int_e^\infty\frac{k}{x(lnx)^{k+1}} dx = 1
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  2. #2
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    Re: Improper Integral Problem

    Quote Originally Posted by mastermin346 View Post
    if k>0 ,show that \int_e^\infty\frac{k}{x(lnx)^{k+1}} dx = 1

    What is the derivative of \frac{-1}{(\ln(x))^k}~?
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  3. #3
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    Re: Improper Integral Problem

    \frac{{}k (ln (x))^{-k-1}}{x}?
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    Re: Improper Integral Problem

    Quote Originally Posted by mastermin346 View Post
    \frac{{}k (ln (x))^{-k-1}}{x}?

    OR \frac{k (ln (x))^{-k-1}}{x}=\frac{k}{x(ln (x))^{k+1}}

    So now you know the anti-derivative. Use it to find the integral.
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  5. #5
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    Re: Improper Integral Problem

    thanks Plato! i got it !
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