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 Tiome_nguyen March 19th, 2011 10:58 PM

crazy partial fraction integral

integral of (x)dx/((3x+7)^3)

i have no idea how to solve for this integral , i'm learning integral by partial fraction and this is the hardest one that i can't do :( , if u know how to solve , please help me , thank you so much

 aswoods March 20th, 2011 03:01 AM

Re: crazy partial fraction integral

$\int\frac{x}{(3x+7)^3}\mathrm{d}x$

Don't use partial fractions for this one, just set u = 3x+7, so du = 3 dx and x = (u-7)/3.

$\frac13\int\frac{\frac13u-\frac73}{u^3}\mathrm{d}u \\= \frac19\int u^{-2}-7u^{-3}\mathrm{d}u\\
=\frac19\left[\frac{1}{-1}u^{-1}-\frac{7}{-2}u^{-2}\right]+c\\
=-\frac{1}{9u}+\frac{7}{18u^2}+c\\
=-\frac{1}{9(3x+7)}+\frac{7}{18(3x+7)^2}+c$

 Tiome_nguyen March 25th, 2011 07:53 PM

Re: crazy partial fraction integral

thank you so much, why didn't i think about using u substitution !!! :)

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