1) x^2-3x-4=0 (x-4)(x+1)=0
1/(x-4)(x+1)=1/5(x-4)-1/5(x+1)
=1/5(ln|x-4|-ln|x+1|)+C=(1/5)ln(|x-4|/|x+1|)+C
x^3/(x-1)=(x^3-1)/(x-1)+1/(x-1)=x^2+1+x+1/(x-1)
=x^3/3+x^2/2+x+ln|x-1|+C
3)2(x+3)/(x-5)(x-1)
A/(x-5)+B/(x-1)=(Ax+Bx-A+5B)/(x-5)(x-1)
A+B=1 A=1-B
5B-A=3 5B-1+B=3 B=2/3 A=1/3
1/3(x+5)+2/3(x+1)
=2/3ln|x+5|+4/3ln|x+1|+C