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Fay

latihan integral fungsi rasional

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\(\int\frac{dx}{x(x+1)(x+2)(x+3)....(x+n)}\)sudah sampai n, gimanah ya kaks......

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Edited by Fay
ada yang lebih

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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

 

  $\displaystyle \int{{Sdx}}=\frac{1}{{n!}}\sum\limits_{{k=0}}^{n}{{{{{\left( {-1} \right)}}^{k}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right)\int{{\frac{{dx}}{{x+k}}}}}}=\frac{1}{{n!}}\sum\limits_{{k=0}}^{n}{{{{{\left( {-1} \right)}}^{k}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right)\ln \left( {x+k} \right)}}+c$

Edited by Paryadi
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