Question

Evaluate: $\int \frac{dt}{t(t+1)}$

Answer 1

$\int \frac{dt}{t(t+1)}$

$=\int \frac{(t+1-t)dt}{t(t+1)}$

$=\int \frac{(t+1)dt}{t(t+1)}-\int \frac{tdt}{t(t+1)}$

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

$=\log \left|t\right|-\log |t+1|+c$

$=\log \left|\frac{t}{t+1}\right|+c$