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

Explanation

`sin=frac{2 tan x/2}{1+tan^2x/2}`

`=int frac{1}{5-4(frac{2tanx/2}{1+tan^2x/2})}dx`

`=int frac{1+tan^2x/2}{5(1+tan^2x/2)-4(2tan x/2)}dx`

On replacing `(1 + tan^2x)/2` in numerator by `sec^2x/2`

`=int frac{sec^2x/2}{5+5tan^2x/2-8tanx/2}dx`

On putting `tan (x/2) = t` and `sec^2(x/2) dx = 2dt`

`=int frac{2dt}{5+5t^2-8t}`

`=2/5 int frac{1}{(t-4/5)^2(3/5)^2}dt`
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