How to integrate this? #intcolor(white).(3x^2-x+1)/(x^3-x^2)# Calculus Introduction to Integration Integrals of Rational Functions 1 Answer dhilak Mar 11, 2018 #3lnabs(x-1)+1/x+C# Explanation: #int(3x^2-x+1)/(x^3-x^2)dx=int(3x^2)/(x^2(x-1))dx -int(x-1)/(x^2(x-1))dx=int(3)/((x-1))dx-int1/x^2dx=3lnabs(x-1)+1/x+C# Answer link Related questions How do you integrate #(x+1)/(x^2+2x+1)#? How do you integrate #x/(1+x^4)#? How do you integrate #dx / (2sqrt(x) + 2x#? What is the integration of #1/x#? How do you integrate #(1+x)/(1-x)#? How do you integrate #(2x^3-3x^2+x+1)/(-2x+1)#? How do you find integral of #((secxtanx)/(secx-1))dx#? How do you integrate #(6x^5 -2x^4 + 3x^3 + x^2 - x-2)/x^3#? How do you integrate #((4x^2-1)^2)/x^3dx #? How do you integrate #(x+3) / sqrt(x) dx#? See all questions in Integrals of Rational Functions Impact of this question 1528 views around the world You can reuse this answer Creative Commons License