Integrate: dx / (5 - 4 sin x) Share with your friends Share 2 Varun.Rawat answered this Let I = ∫dx5 - 4 sin x=∫dx5 - 42 tan x/21 + tan2x/2=∫1 + tan2x/25 + 5 tan2x/2 - 8 tanx/2 dx=∫sec2x/25 tan2x/2 - 8 tan x/2 + 5 dxput tan x2 = t⇒sec2x2 dx = 2 dtSo, I = 2∫dt5t2 - 8t + 5=25∫dtt2 - 85t + 1=25∫dtt2-8t5+1625+1-1625=25∫dtt-452 - 352=25 × 56 log t-45-35t-45+35 + C=13logt-75t-15 + C=13 log5 tan x/2 - 75 tanx/2 - 1 + C 1 View Full Answer