∫(x^5+x^4-8）／x^3-xdx求不定积分具体过程

Question

∫(x^5+x^4-8）／x^3-x dx求不定积分具体过程

Answer 1

∫(x^5+x^4-8）／(x^3-x)dx
=S(x^5-x^3+x^4-x^2+x^3-x+x^2-1+x-1-6)(x^3-x)dx
=S(x^2+x+1+1/x+1/x(x+1)-6/(x^3-x))dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x))-6S1/(x^3-x)dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x)-3S(1/(x-1)-2/x+1/(x+1))dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x)-3ln(x-1)+6lnx-3ln(x+1)+c
=1/3*x^3+1/2*x^2+x+8lnx-4ln(1+x)-3ln(x-1)+c