int (3x-7)dx/(x^3+4x^2+4x+16)=
=int{(19/20) *x/(x^2+4) - (4/5)/(x^2+4) - (19/20)/(x+4)} dx=
=(19/20)int xdx/(x^2+4)-(4/5)int dx/(x^2+4)-(19/20)int dx/(x+4)=...

Найдите каждый интеграл отдельно
int xdx/(x^2+4)=...
int dx/(x^2+4)=...
int dx/(x+4)=...
и подставьте.