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Evaluate: int1/(5-4sinx)\ dx...

Evaluate: `int1/(5-4sinx)\ dx`

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`int1/(5-4sinx)\ dx`
`sinx=frac{2 tan x/2}{1+tan^2 x/2}`
`=int frac{1+tan^2 x/2}{5(1+tan^2 x/2)-4(2tan x/2)}dx`
`=int frac{sec^2 x/2}{5+5tan^2 x/2-8tanx/2}dx`
On putting `tan (x/2) = t` and `sec^2(x/2) dx = 2dt`
`=2/5 int frac{1}{(t-4/5)^2+(3/5)^2}dt`
`=2/3 tan^(-1)(frac{5 tan x/2-4}{3})`
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