Evaluate: `int(sinx)/(sin3x)dxdot`

Explanation

We have `int(sinx)/(sin3x)dx=int(sinx)/((3sinx-4sin^(3)x))dx`
`=int(1)/((3-4sin^(2)x))dx` [ diving num . And denom . By sin x]
`=int(sec^(2)x)/(3sec^(2)x-4tan^(2)x)dx` [ dividing num . And denom . By ` cos^(2)x`]
`=int(sec^(2)x)/(3(1+tan^(2)x)-4tan^(2)x)dx=int(sec^(2)x)/((3-tan^(2)x))dx`
`=int(dt)/((3-t^(2)))`, where tan x = t and `sec^(2)xdx =dt`
`=int(dt)/([(sqrt(3))^(2)-t^(2)])=(1)/(2sqrt(3))log|(sqrt(3)+t)/(sqrt(3)-t)|+C`
`=(1)/(2sqrt(3))log|(sqrt(3)+tanx)/(sqrt(3)-tanx)|+C`.