∫dx(7x^2-x+1/x^3+1)求不定积分?

∫(7x²-x+1)/(x³+1)dx
=∫[(4x-2)/(x²-x+1)+3/(x+1)]dx
=∫(4x-2)/(x²-x+1)dx+3∫1/(x+1)dx
①求∫(4x-2)/(x²-x+1)dx
令u=x²-x+1,则du=2x-1 dx
∫(4x-2)/(x²-x+1)dx
=∫2/u·du
=2lnu
=2ln(x²-x+1)+C1
②求3∫1/(x+1)dx
3∫1/(x+1)dx
=3ln(x+1)+C2
所以 ∫(7x²-x+1)/(x³+1)dx=2ln(x²-x+1)+3ln(x+1)+C