Evaluate: `int1/(4+3tanx)\ dx`

Explanation

We have given

`int1/(4+3tanx)\ dx`

`I=int(cosx)/(3sinx+4cosx)`

`(cosx)=A(3sinx+4cosx)+B[d/(dx)(3sinx+4cosx)]`

`(cosx)=A(3sinx+4cosx)+B(-4sinx+3cosx)`

On comparing sinx and cosx coefficients and solving them we get

`A=3/25,B=4/25`

`I=int(3/25(3cosx-4cosx)+4/25(4cosx+3sinx))/(4cosx+3sinx)dx`

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