7.1 Integration Techniques
Integration by Parts
Question #5 (Hard): Reduction Formula
Reduction formula means a function that is raised to power of n can be recursively written in term of
the function with lower power, and repeating the process, the integral can be eventually solved.
To prove reduction formula, split the power into and , or even and depending on the
function and its derivative (such as tangent, cotangent, cosecant, secant). Then apply integration by
parts, simplify, and in the process there is a term which can be moved to the other side to be combined
with the original integral. From there on through further simplifying process, the reduction formula is
Prove the reduction formula using integration by parts.
∫ ( ) ∫
Based on integration by part