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Posted January 18th, 2010 by alpha
in

$ \int \frac{x^2}{(a+bx)^2}.dx $

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answer

On January 19th, 2010 Structure says:
$$ \int \frac{x^2}{(a+bx)^2}.dx=\frac{1}{b^2} \int \frac{((bx+a)-a)^2}{(a+bx)^2}.dx=\frac{1}{b^2} \int \frac{(bx+a)^2-2a(bx+a)+a^2}{(a+bx)^2}.dx=\frac{1}{b^2} \int( 1-\frac{2a}{a+bx}+\frac{a^2}{(a+bx)^2})dx $$

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