1/1+x^3 .dx

Thank you.

dear balaram

1+x³ = (1+x)(1+x²-x)

now integral becomes

I = dx/(1+x)(1+x²-x)

now use partial fraction 

1/(1+x)(1+x²-x) = A/(1+x) + (Bx+c)/(1+x²-x)

find A,B,C & then integrate it ...

approve my ans if u like it