Mathematics

Mathematics

Problem

∫dx5+4cos⁡x=\int \frac{dx}{5+4\cos x} = (a) 23tan⁡−1(13tan⁡x)+c\frac{2}{3}\tan^{-1}\left(\frac{1}{3}\tan x\right)+c (b) 13tan⁡−1(13tan⁡x)+c\frac{1}{3}\tan^{-1}\left(\frac{1}{3}\tan x\right)+c (c) 23tan⁡−1(13tan⁡x2)+c\frac{2}{3}\tan^{-1}\left(\frac{1}{3}\tan\frac{x}{2}\right)+c (d) 13tan⁡−1(13tan⁡x2)+c\frac{1}{3}\tan^{-1}\left(\frac{1}{3}\tan\frac{x}{2}\right)+c (a) 23tan⁡−1(13tan⁡x)+c\frac{2}{3}\tan^{-1}\left(\frac{1}{3}\tan x\right)+c (b) 13tan⁡−1(13tan⁡x)+c\frac{1}{3}\tan^{-1}\left(\frac{1}{3}\tan x\right)+c (c) 23tan⁡−1(13tan⁡x2)+c\frac{2}{3}\tan^{-1}\left(\frac{1}{3}\tan\frac{x}{2}\right)+c (d) 13tan⁡−1(13tan⁡x2)+c\frac{1}{3}\tan^{-1}\left(\frac{1}{3}\tan\frac{x}{2}\right)+c

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