or you may use partial fractions alternatively, what i mean is
t-1 / t^2 +4t +3
= 1/2 ( 2t - 2)/(t^2 +4t +3)
=1/2 ( 2t +4 -6)/(t^2 +4t +3)
= 1/2 ( 2t +4)/(t^2 +4t +3) - 1/2 (6/(t^2 +4t +3))
integrate separately, for 1st part, if you let denominator =z,. you directly get numerator = dz ..
we are concerned with integrating 1/(t^2 +4t +3)
that's also simple, we see we have
1/(t+1)(t+3) = 1/2 (2 / (t+1)(t+3))
=1/2 ( t+3 - (t+1))/(t+1)(t+3))
=>now when you separate out, you'll directly be able to integrate ..hope that helps..
note that i've used partial fractions only,but in a different manner..