ज्ञात करें `int (sin x)/(sin 3x)dx`

Explanation

`I =int (sin x)/(sin 3x)dx=int (sinx)/(3sinx-4sin^3x)dx=int(dx)/(3-4sin^2 x)`
`int =(sec^2 x)/(3sec^2 x -4 tan^2x)dx = int (sec^2x)/(3-tan^2x)dx`
`z=tanx` रखे, तो `dz=sec^2 xdx`
अब, `I=int (dz)/((sqrt3)^2-z^2)=1/(2sqrt3)log|(sqrt3+z)/(sqrt3-z)|+c=1/(2sqrt3)"log"|(sqrt3+tanx)/(sqrt3-tanx)|+c`