Let ∫2−tan⁡x3+tan⁡x dx=12 (αx+log⁡e∣βsin⁡x+γcos⁡x∣)+C\int \frac{2 - \tan x}{3 + \tan x}\,dx = \frac{1}{2}\,(\alpha x + \log_e |\beta \sin x + \gamma \cos x|) + C…

Mathematics

Problem

Let ∫2−tan⁡x3+tan⁡x dx=12 (αx+log⁡e∣βsin⁡x+γcos⁡x∣)+C\int \frac{2 - \tan x}{3 + \tan x}\,dx = \frac{1}{2}\,(\alpha x + \log_e |\beta \sin x + \gamma \cos x|) + C, where CC is the constant of integration. Then, α+γβ\alpha + \frac{\gamma}{\beta} is equal to (a) 1 (b) 3 (c) 7 (d) 4

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