How do you integrate #int (3x + 2) / [(x - 1)(x + 4)] # using partial fractions? Calculus Techniques of Integration Integral by Partial Fractions 1 Answer Konstantinos Michailidis Feb 21, 2016 We have that #(3x+2)/[(x-1)(x+4)]=2/(x+4)+1/(x-1)# Hence #int (3x+2)/[(x-1)(x+4)]dx=int 2/(x+4)dx+int 1/(x-1)dx= 2*logabs(x+4)+logabs(x-1)+c# Answer link Related questions How do I find the partial fraction decomposition of #(2x)/((x+3)(3x+1))# ? How do I find the partial fraction decomposition of #(1)/(x^3+2x^2+x# ? How do I find the partial fraction decomposition of #(x^4+1)/(x^5+4x^3)# ? How do I find the partial fraction decomposition of #(x^4)/(x^4-1)# ? How do I find the partial fraction decomposition of #(t^4+t^2+1)/((t^2+1)(t^2+4)^2)# ? How do I find the integral #intt^2/(t+4)dt# ? How do I find the integral #int(x-9)/((x+5)(x-2))dx# ? How do I find the integral #int1/((w-4)(w+1))dw# ? How do I find the integral #intdx/(x^2(x-1)^2)# ? How do I find the integral #int(x^3+4)/(x^2+4)dx# ? See all questions in Integral by Partial Fractions Impact of this question 1230 views around the world You can reuse this answer Creative Commons License