Evaluate: `int(cosx)/(cos3x)dx`

Explanation

`int frac{cosx}{cos3x}dx`

`=int frac{cosx}{4cos^3x-3cosx}dx`

`=int 1/(4cos^2x-3)dx`

Dividing the numerator and denomenator by `cos^2x`

`=int frac{sec^2x}{3-4sec^2x}dx`

`=int frac{sec^2x}{4-3-3tan^2x}dx`

`=int frac{sec^2x}{1-3tan^2x}dx`

`x=t` and `sec^2xdx=dt`
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