\(\int\frac{3sinx}{3 + 4cosx}dx\)

= \(\int\frac{3\frac{dt}{-4}}{t} = \frac{-3}{4}\int\frac{1}{t}dt\)

= \(\frac{-3}{4}\)log t + c 

= \(\frac{-3}{4}\)log(3 + 4 cos x) + c 

put 3 + 4 cos x = t 

– 4 sinx dx = dt 

sin x dx = \(\frac{dt}{-4}\)