If ∫1sin⁡x+4(sin⁡x-1) dx=A 1tan⁡x2-1+Btan-1⁡fx+C1. Then, which of the following is true about A, B and f(x).

Question

\int \frac{1}{(\sin x + 4) (\sin x - 1)} d x = A \frac{1}{\tan \frac{x}{2} - 1} + B \tan^{- 1} (f (x)) + C_{1}

. Then, which of the following is true about

A, B

and

f (x) .

A = \frac{1}{5}, B = \frac{- 2}{5 \sqrt{15}}, f (x) = \frac{4 \tan x + 3}{\sqrt{15}}

A = - \frac{1}{5}, B = \frac{1}{\sqrt{15}}, f (x) = \frac{4 \tan (\frac{x}{2}) + 1}{\sqrt{15}}

A = \frac{2}{5}, B = \frac{- 2}{5}, f (x) = \frac{4 \tan x + 1}{5}

A = \frac{2}{5}, B = \frac{- 2}{5 \sqrt{15}}, f (x) = \frac{4 \tan \frac{x}{2} + 1}{\sqrt{15}}

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