If `int_0^(pi/3)(cosx)/(3+4sinx) dx=k log((3+2sqrt(3))/3),` then `k` is equal to

Explanation

Given:`int_0^(pi/3)(cosx)/(3+4sinx) dx=k log((3+2sqrt(3))/3)`

We have to find k

`I=int_0^(pi/3)(cosx)/(3+4sinx) dx`

Let `t=3+4sinx implies dt=4cosxdx`

When `x=0 implies t=3` and when `x=pi/3 implies t=3+2sqrt3`

Then

`I=1/4int_3^(3
+2sqrt3) 1/t dt`

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