Category:Primitive of Reciprocal of p plus q by Sine of a x

This category contains pages concerning Primitive of $\dfrac 1 {p + q \sin a x}$:

$\ds \int \frac {\d x} {p + q \sin a x} = \begin{cases}

\ds \frac 2 {a \sqrt {p^2 - q^2} } \map \arctan {\frac {p \tan \dfrac {a x} 2 + q} {\sqrt {p^2 - q^2} } } + C & : q^2 - p^2 < 0 \\ \ds \frac 1 {a \sqrt {q^2 - p^2} } \ln \size {\frac {p \tan \dfrac {a x} 2 + q - \sqrt {p^2 - q^2} } {p \tan \dfrac {a x} 2 + q + \sqrt {p^2 - q^2} } } + C & : q^2 - p^2 > 0 \\ \end{cases}$