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Math Help - Reduction formula

  1. #1
    Junior Member symstar's Avatar
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    Reduction formula

    I need to use the reduction formula for this problem.
    \int(\ln{x})^{n} dx where n\geqslant{2}

    Would these be the best choices for the integration?
    u=(\ln{x})^{n-1}
    du=(\tfrac{1}{x})(n-1)(\ln{x})^{n-2} dx
    dv=\ln{x} dx
    v=x\ln{x}-x
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by symstar View Post
    I need to use the reduction formula for this problem.
    \int(\ln{x})^{n} dx where n\geqslant{2}

    Would these be the best choices for the integration?
    u=(\ln{x})^{n-1}
    du=(\tfrac{1}{x})(n-1)(\ln{x})^{n-2} dx
    dv=\ln{x} dx
    v=x\ln{x}-x
    No.

    Let I_n = \int (\ln x)^{n} \, dx.

    Use the choice u = (\ln x)^{n} and dv = dx.

    Then I_n = x \, (\ln x)^n - n I_{n-1} \, ....
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