Integrating hyperbolic functions

Hyperbolic functions are analogues of the standard circular functions (such as sin, cos, and tan), but are applied to hyperbolic geometry instead of circular geometry.
The indefinite integrals of the hyperbolic functions sinh(x), cosh(x), and tanh(x) are simple and analogous to those of their circular counterparts.
The integral of sinh(x) is cosh(x) + C, where C is the constant of integration. This is similar to the integral of sin(x), which is -cos(x) + C.
The integral of cosh(x) is sinh(x) + C, which parallels the integral of cos(x), being sin(x) + C.
The integral of tanh(x) is ln cosh(x) + C, which differs from the integral of tan(x).
To integrate coth(x) and sech(x), one has to use some identities or change the form of the function before integration.
The integral of sech^2(x) is tanh(x) + C. This requires the use of trigonometric identities or substitution to be solved.
The integral of sech(x)tan(x) is -sech(x) + C, which is another example of an integral that requires the use of identities or substitution to be solved.
Co-functions (such as csch(x) and sech(x)) and their integrals can be derived using the definitions of the hyperbolic functions and methods such as integration by parts or substitution.
Practice problem-solving skills using a variety of sources, to ensure full understanding of the different methods used to integrate hyperbolic functions.
Familiarity with the properties and graphs of hyperbolic functions can help to visualise the problem and select the appropriate method of integration.
Routine practice is key to fully understand how to integrate hyperbolic functions, as often the method of integration will not be immediately clear.
Understanding when and how to use substitution will significantly help with integrating more complex hyperbolic functions.