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

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SUMMARY

The integral of (x^2+x)/(2x+1) can be simplified by breaking it into manageable parts. The expression can be rewritten as (x^2+(1/2)x)/(2x+1) + (x/(4x+2)), leading to the components (x/2) + (1/4) - (1/(16x+8)). This method utilizes the technique of partial fraction decomposition to facilitate integration. The final result provides a clearer path to solving the integral.

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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...
 
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What (rules) do you know about integration?
 
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]
 

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