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

[Sua Lee]

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]

What (rules) do you know about integration?

 

[mathman]

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