Evaluate: `int1/(13+3cosx+4sinx)dx`

Explanation

`I=frac{1}{13+3 cos x+4 sin x} dx`


We know that,


`sin x=frac{2 tan frac{x}{2}}{1+tan ^{2} frac{x}{2}} text { and } cos x=frac{1-tan ^{2} frac{x}{3}}{1+tan ^{2} frac{x}{2}} `

`Rightarrow int frac{1}{13+4 sin x+3 cos x} d x `

`=int frac{1}{13+4(frac{2 tan frac{x}{2}}{1+tan ^{2} frac{x}{2}})+3(frac{.1-tan ^{2} frac{x}{2})}{1+tan ^{2 frac{x}{2}}})} d x `

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