∫x^5dx/(1+x^3)
= ∫[(x^5+x^2-x^2)/(1+x^3)]dx
= ∫[x^2-x^2/(1+x^3)]dx
= x^3/3-(1/3)∫[1/(1+x^3)]d(1+x^3)
= x^3/3-(1/3)ln|1+x^3|+C
∫x^5dx/(1+x^3)
= ∫[(x^5+x^2-x^2)/(1+x^3)]dx
= ∫[x^2-x^2/(1+x^3)]dx
= x^3/3-(1/3)∫[1/(1+x^3)]d(1+x^3)
= x^3/3-(1/3)ln|1+x^3|+C