∫1/(x²+5x+4)dx
=∫1/[(x+1)(x+4)] dx
=(1/3)[∫1/(x+1) dx-∫1/(x+4) dx]
=(1/3)ln|x+1|-(1/3)ln|x+4|+C
=(1/3)ln|(x+1)/(x+4)|+C