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  1. Top | #1

    Jun 2013
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  3. Top | #2

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    $\LARGE {\color{DarkRed} (1)\int \frac{2x}{(1+x)^{2}}dx=2\int \frac{x+1-1}{(x+1)^{2}}dx}$
    ${\color{DarkRed} =2[\int \frac{1}{(x+1)}dx-\int \frac{1}{(x+1)^{2}}dx]}$
    ${\color{DarkRed} =2[ln(x+1)+\frac{1}{x+1}]+c}$

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    [SIZE=4]$\LARGE {\color{Cyan} (2)\int \frac{4}{xln3x}dx ,,,put,y=ln3x\rightarrow dy=\frac{1}{x}dx}$[/SIZE]
    ${\color{Cyan} \Rightarrow I=4\int \frac{1}{y}dy=4lny+c=4lnln3x+c}$

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  7. Top | #4

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    $\LARGE {\color{Red} (3)\int \frac{(1+lnx)^{2}}{x}dx=\frac{(1+lnx)^{3}}{3}+c,,} $

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