Primitive of Reciprocal of p plus q by Hyperbolic Tangent of a x

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {p + q \tanh a x} = \frac {p x} {p^2 - q^2} - \frac q {a \left({p^2 - q^2}\right)} \ln \left\vert{q \sinh a x + p \cosh a x}\right\vert + C$

Also see

 * Primitive of $\dfrac 1 {p + q \sinh a x}$


 * Primitive of $\dfrac 1 {p + q \cosh a x}$


 * Primitive of $\dfrac 1 {p + q \coth a x}$


 * Primitive of $\dfrac 1 {q + p \operatorname{sech} a x}$


 * Primitive of $\dfrac 1 {q + p \operatorname{csch} a x}$