Some help with this please! Evaluate the integral using A/(x-3) +B/(X+1) + C/(x-4)?

Numerator of the integrand is 3x^2-12x+5

so after splitting into partial fractions we have A/x-1+B/x-4+C/x-3

once you do the arithmetic it comes to :

A+B+C=3

-7A-2B-3C=-12

12A-3B-4C=5

The determinant of the coefficients is -20

Using Cramer's rule we get A=-1 B=-5/2 and C=13/2

so after the integration we have -ln(x+1)-(5/2)ln(x-4)+(13/2)ln(x-3)+C

so answer is ln(x+1)^(-1)-ln(x-4)^(5/2)+ln(x-5)^(13/2)+lnC you can reduce this to one log but it will not help too much!