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the main problem im having is i cant figure out how they simplified this equation. Ill try and use latex but its my first time so i dont know if it will work.

[tex]

\int(1-\frac{1}{3(x+1)}+\frac{(x-2)}{3(x^2-x+1)}) dx

[/tex]

and somehow this simplifies to this

[tex]

x- (1/3)ln(abs(x+1)) +(1/6) \int \frac{(2x-1)}{(x^2-x+1)} dx - (1/2) \int \frac{(dx)}{(x-.5)^2+(3/4)}

[/tex]

i understand how to get the x-(1/3)ln(2x-1) but i dont get how they seperated the other two terms for integration. or how they pulled out (1/6)

[tex]

\int(1-\frac{1}{3(x+1)}+\frac{(x-2)}{3(x^2-x+1)}) dx

[/tex]

and somehow this simplifies to this

[tex]

x- (1/3)ln(abs(x+1)) +(1/6) \int \frac{(2x-1)}{(x^2-x+1)} dx - (1/2) \int \frac{(dx)}{(x-.5)^2+(3/4)}

[/tex]

i understand how to get the x-(1/3)ln(2x-1) but i dont get how they seperated the other two terms for integration. or how they pulled out (1/6)

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