Question

Integrate 1/cosx+•3sinx DX =

Answer 1

Given,

∫  1 / cosx + √3 sinx dx

Let √3 = i sin  Ф and 1 = i cos Ф

Then,  ∫  1 / ( i sin  Ф sin x + i cosФ cosx ) dx

=  1/ i ∫ dx / (cos x - Ф)

= 1 / i  ∫  sec(x - Ф) dx

= 1 / i log | tan ( π/4 + x/2 - Ф/2) | + C

= 1 / 2 log | tan (π/4 + x/2 - π/6) | + C

= 1/2 log | tan ( x / 2 + π / 12) | + C