Complex functions require manipulation so the expression can be re-written in a form that fits one of the 'general' rules for integration. There is one general approach for integrating expressions which multiply sine and cosine functions raised to a power. For example:
$\int {cos}^{3}x\phantom{\rule{3px}{0ex}}{sin}^{4}x\phantom{\rule{3px}{0ex}}dx$
We can use a general approach when the exponent for cosine is odd.
When integrating a function of this form:
• Break the cosine into the product that has one term as 'cos x' x
• Rewrite the equation in terms of sine (as much as possible)
• Use substitution to simplify the equation in simpler terms.
Recipe: COS Raised to Odd-Numbered Power