## Integrating Reciprocal Trigonometric and Hyperbolic Functions

All the the reciprocal trigonometric and hyperbolic functions can be integrated by manipulating them into the form

differentiates to giveanddifferentiates to give giveso the numerator of the inegrand is the derivative of the denominator, hence

differentiates to giveanddifferentiates to giveso the numerator of the integrand is the derivative of the denominator, hence

SubstitutesoThe integral becomes

SubstitutesoThe integral becomes