integral of (1 - x + 2x^2 - x^3) / (x(x^2 + 1)^2) dx

[kapplayer]

what would be the best method to start with for the integral of (1-x+2x^2-x^3)/(x(x^2+1)^2)dx, i tried partial fraction but had a big mess. thanks

 

[Deleted member 4993]

Re: integrate

what would be the best method to start with for the integral of (1-x+2x^2-x^3)/(x(x^2+1)^2)dx, i tried partial fraction but had a big mess. thanks

\(\displaystyle 1 - x + 2x^2 - x^3 = (x^2 + 1)(2-x) - 1\)

I have not done it - but I would have tried substitution

\(\displaystyle x \, = \, tan(\theta)\)

 

[kapplayer]

thanks for the help
is this correct so far
so now i get ln|sino| - (sin^2o/2) - o + c
sino = x/(x^2+1)^(1/2)
ln|sino| = ln|x/(x^2+1)^(1/2)|
(sin^2o/2) = x^2/(2(x^2+1))
what does o =