Primitive of Reciprocal of Sine of a x plus Cosine of a x/Examples/sin x + cos x

Example of Use of Primitive of $\dfrac 1 {\sin a x + \cos a x}$

 * $\ds \int \dfrac {\d x} {\sin x + \cos x} = \frac 1 {\sqrt 2} \ln \size {\map \cosec {x + \frac \pi 4} - \map \cot {x + \frac \pi 4} } + C$

Proof
From Primitive of $\dfrac 1 {\sin a x + \cos a x}$:

The result follows on setting $a = 1$.