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Let $f (x) = \frac{1}{4 - 3 \cos^{2} x + 5 \sin^{2} x}$ and if its antiderivative $F (x) = (1 / 3) \tan^{- 1} (g (x)) + C$ then $g (x)$ is
equal to

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3tan⁡x

(2)tan⁡x

2tan⁡x

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Correct option is A

F(x)=∫dx4−3cos2⁡x+5sin2⁡x+C=∫sec2⁡xdx41+tan2⁡x−3+5tan2⁡x+C=∫dt9t2+1+C=13tan−1⁡3t+C (t=tan⁡x)Therefore g(x)=3tan⁡x

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Let f(x)=14−3cos2⁡x+5sin2⁡x and if its antiderivative F(x)=(1/3)tan−1⁡(g(x))+C then g (x) isequal to

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Let $f (x) = \frac{1}{4 - 3 \cos^{2} x + 5 \sin^{2} x}$ and if its antiderivative $F (x) = (1 / 3) \tan^{- 1} (g (x)) + C$ then $g (x)$ is
equal to