10. Reduction Formulae

You may have noticed in the Table of Integrals that some integrals are given in terms of a simpler integral. These require a few steps to find the final answer.

Reduction formulae are integrals involving some variable $n$, as well as the usual $x$. They are normally obtained from using integration by parts.

We use the notation $I_{n}$ when writing reduction formulae.

Example 1

Given that

MATH MATH,

find $\int \sin ^{4}x$ $dx$.


Answer


Example 2

Given that if MATH $dx$, $\ $then MATH.

Find $\int \tan ^{3}x$ $dx$.


Answer



See the Scientific Notebook version of the same Examples. (info: math expression).



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