Category:Examples of Use of Primitive of Reciprocal of p plus q by Cosine of a x

This category contains examples of use of Primitive of $\dfrac 1 {p + q \cos a x}$.

$\ds \int \frac {\rd x} {p + q \cos a x} = \begin {cases}

\dfrac 2 {a \sqrt {p^2 - q^2} } \map \arctan {\sqrt {\dfrac {p - q} {p + q} } \tan \dfrac {a x} 2} + C & : p^2 > q^2 \\ \dfrac 1 {a \sqrt {q^2 - p^2} } \ln \size {\dfrac {\tan \dfrac {a x} 2 + \sqrt {\dfrac {q + p} {q - p} } } {\tan \dfrac {a x} 2 - \sqrt {\dfrac {q + p} {q - p} } } } + C & : p^2 < q^2 \\ \end {cases}$ for $p \ne q$.