What is the integral of (x^2+x)/(2x+1) when split into manageable pieces?

Sua Lee · Nov 26, 2016

I know integral of (2x+1)/(x^2+x).
but i don't know integral of (x^2+x)/(2x+1).
I'm very curious...
please answer me...

fresh_42 · Nov 26, 2016

What (rules) do you know about integration?

mathman · Nov 26, 2016

Split the integrand into manageable pieces.
[itex]\frac{x^2+x}{2x+1}[/itex]=[itex]\frac{x^2+\frac{x}{2}}{2x+1}+\frac{x}{4x+2}[/itex]=[itex]\frac{x}{2}+\frac{x+\frac{1}{4}}{4x+2}-\frac{1}{16x+8}[/itex]=[itex]\frac{x}{2}+\frac{1}{4}-\frac{1}{16x+8}[/itex]

What is the integral of (x^2+x)/(2x+1) when split into manageable pieces?

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What is the integral of (x^2+x)/(2x+1) when split into manageable pieces?

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