Question

Integral of (3t-2)/(t+1).

Answer 1

$\int { \frac{3t-2}{t+1} } \, dt = 3 \int { \frac{t+1-1}{t+1} } \, dt - 2 \int { \frac{1}{t+1} } \, dt = \\ 3( - \int { \frac{1}{t-1} } \, dt + \int {1} \, dt ) - 2 ln ( t + 1 ) = \\ -3ln(t+1)+3t-2ln(t+1)=$
= 3 t - 5 ln( t +1) + C