Question

Evaluate the integral \int (3t-2)/(t-1)dt please which method i should use

Answer 1

$\dfrac{3t-2}{t-1}=\dfrac{3(t-1)+1}{t-1}=3+\dfrac1{t-1}$

$\displaystyle\int\frac{3t-2}{t-1}\,\mathrm dt=3\int\mathrm dt+\int\frac{\mathrm dt}{t-1}=3t+\ln|t-1|+C$