useful formula
========
∀a∈R^+ :∀b ∈R: a sin x +b cos x =(√(a^2 +b^2 ))sin (x+arctan (b/a))
∫(dx/(a sin x +b cos x))=
=(1/(√(a^2 +b^2 )))∫(dx/(sin (x+arctan (b/a))))=
[t=x+arctan (b/a) → dx=dt]
(1/(√(a^2 +b^2 )))∫(dt/(sin t))=−(1/(√(a^2 +b^2 )))ln ((1/(sin t))+(1/(tan t))) =
=−(1/(√(a^2 +b^2 )))ln ∣(((√(a^2 +b^2 ))−b sin x +a cos x)/(a sin x +b cos x))∣ +C