Why am i getting two different answers for two different ways of solving the integral.

Question

So the Integral is $$\int \frac {dt}{t(t+1)^2}$$ So i thought of it two ways.

1.Substituting $\displaystyle y=\frac 1t$

Solution: $\displaystyle \ln\left|\frac{t}{1+t}\right|-\frac{t}{1+t}$

2.Substituting $\displaystyle y=\frac {1}{1+t}$

Solution: $\displaystyle \ln\left|\frac{t}{1+t}\right|+\frac {1}{1+t}$

Here's the photo for reference enter image description here

Answer 1

1.Substituting $\displaystyle y=\frac 1t$

Solution: $\displaystyle \ln\left|\frac{t}{1+t}\right|-\frac{t}{1+t}$

2.Substituting $\displaystyle y=\frac {1}{1+t}$

Solution: $\displaystyle \ln\left|\frac{t}{1+t}\right|+\frac {1}{1+t}$

Note that:

$$\frac{1}{1+t}=-\frac{t}{1+t}+1$$

your two solutions differ by a constant $1$, hence both of them are correct.