All the the reciprocal trigonometric and hyperbolic functions can be integrated by manipulating them into the form
differentiates to give
and
differentiates to give give
so the numerator of the inegrand is the derivative of the denominator, hence
differentiates to give
and
differentiates to give
so the numerator of the integrand is the derivative of the denominator, hence
Substitute
so
The integral becomes
SubstitutesoThe integral becomes
