I'm having trouble integrating x/(x^3+1)

here's what I did

x/[(x+1)(x^2-x+1)] I did partial fractions

A/(x+1) + (Bx+C)/(x^2-x+1)

A+B=0, A+C=0, -A+B+C=1

A=-1/3 , B=C=1/3

then I got

-(1/3)ln(x+1) + integrand(x+1)/(x^2-x+1)dx

it's supposed to be convergent from 0 to infinity but with that ln there it seems dodgy

Question

I'm having trouble integrating  x/(x^3+1) 

here's what I did 

x/[(x+1)(x^2-x+1)] I did partial fractions

A/(x+1)  +  (Bx+C)/(x^2-x+1) 

A+B=0, A+C=0, -A+B+C=1

A=-1/3 , B=C=1/3 

then I got 

-(1/3)ln(x+1) + integrand(x+1)/(x^2-x+1)dx

it's supposed to be convergent from 0 to infinity but with that ln there it seems dodgy

anonymous · Answer

I have a feeling the partial fraction I did is incorrect