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Showing content with the highest reputation on 02/27/2017 in all areas

  1. 1 point
    Mudah diperiksa dengan partial fraction (gunakan cover up rule) bahwa $\displaystyle S=\prod\limits_{{k=0}}^{n}{{\frac{1}{{x+k}}}}=\frac{1}{{n!}}\sum\limits_{{k=0}}^{n}{{{{{\left( {-1} \right)}}^{k}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right)\frac{1}{{x+k}}}}$ Jadi $\displaystyle \int{{Sdx}}=\frac{1}{{n!}}\sum\limits_{{k=0}}^{n}{{{{{\left( {-1} \right)}}^{k}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right)\int{{\frac{{dx}}{{x+k}}}}}}=\frac{1}{{n!}}\sum\limits_{{k=0}}^{n}{{{{{\left( {-1} \right)}}^{k}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right)\ln \left( {x+k} \right)}}+c$
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