Question

Evaluate $\int \frac{2tdt}{3t+4}$

Answer 1

Consider the given integral.

$I=\int \frac{2t}{3t+4}dt$

$I=\frac{2}{3}\int (1-\frac{4}{3}\frac{1}{(t+\frac{4}{3})})dt$

$I=\frac{2}{3}\int 1dt-\frac{8}{9}\int \frac{1}{(t+\frac{4}{3})}dt$

$I=\frac{2}{3}t-\frac{8}{9}\ln (t+\frac{4}{3})+C$

Hence, this is the answer.