ABSTRACT
Calculus is the most powerful branch of mathematics. It is capable of computing many quantities accurately, which cannot be calculated using any other branch of mathematics. Many integrals are not 'standard' ones that we can determine from a list of results. Some need substitutions to rearrange them into a standard form. There are a number of trigonometric and hyperbolic substitutions that may be used for certain integrals to change them into a form that can be integrated. This chapter helps the reader to integrate functions of the form sin2x, cos2x, tan2x, and cot2x, integrate functions having powers of sines and cosines, and integrate functions that are products of sines and cosines. It also helps the reader to integrate using the sin θ substitution, tan θ substitution, sinh θ substitution, and cosh θ substitution.
