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 sin and cos functions when 'sin' is raised to an odd-numbered power. For example:
$\int {sin}^{3}x\phantom{\rule{3px}{0ex}}{cos}^{2}x\phantom{\rule{3px}{0ex}}dx$
We can use a general approach when the exponent for sine is odd.
When integrating a function of this form:
• Break the sine into the product that has one term as 'sin x' x
• Rewrite the equation in terms of cosine (as much as possible)
• Use substitution to simplify the equation in simpler terms.
Recipe: SIN Raised to Odd-Numbered Power