Integral of x/x^2 + 2x+2: Solving Tips

[apiwowar]

integral of x/x² +2x+2

so the first thing i did was complete the square which gave me

integral of x/(x-1)²+1

then i tried substituting by w=x-1 and dw = dx but that leaves the x on the top.

what am i not seeing?

 

[zachzach]

integral of x/x² +2x+2

so the first thing i did was complete the square which gave me

integral of x/(x-1)²+1

then i tried substituting by w=x-1 and dw = dx but that leaves the x on the top.

what am i not seeing?

\frac{x}{x^2} + 2x +2 = \frac{1}{x} +2x +2

Just do each of those separately.

 

[apiwowar]

my bad its x/(x²+2x+2)

not x/x²+2x+2

 

[zachzach]

Try trigonometric substitution after completing the square. You completing the square is wrong btw, it should be a +.