Integral of 1/(a + b sin x) or 1/(a + b cos x): substitute t = tan(x/2)

1. A.
   $\frac{2}{5}\tan^{-1}\!\left(\frac{5\tan(x/2)+4}{3}\right)+c$
2. B.
   $\frac{2}{3}\tan^{-1}\!\left(\frac{5\tan(x/2)+4}{3}\right)+c$
3. C.
   $\frac{2}{5}\log\!\left|\frac{5\tan(x/2)+7}{5\tan(x/2)+1}\right|+c$
4. D.
   $\frac{2}{3}\log\!\left|\frac{5\tan(x/2)+7}{5\tan(x/2)+1}\right|+c$

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1. A.
   $2\tan^{- 1}\left( \frac{1}{\sqrt{3}}\tan\frac{x}{2} \right) + c$, where $c$ is the constant of integration
2. B.
   $\frac{2}{\sqrt{3}}\tan^{- 1}\left( \frac{1}{\sqrt{3}}\tan\frac{x}{2} \right) + c$, where $c$ is the constant of integration
3. C.
   $\frac{1}{\sqrt{3}}\tan^{- 1}\left( \frac{1}{\sqrt{3}}\tan\frac{x}{2} \right) + c$, where c is the constant of integration
4. D.
   $\sqrt{3}\tan^{- 1}\left( \frac{1}{\sqrt{3}}\tan\frac{x}{2} \right) + c$, where $c$ is the constant of integration

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