Piecewise integration can be used to obtain the reduction formulas for integrals.
These formulas express an integral with function power in terms of an integral that involves a lower power of that function.
For example, if no is a positive integer and no 2, then piecewise integration can be used to obtain the reduction formulas.
To illustrate how these formulas are obtained, let us deduce formula (2).
Transposing the last term to the left side gives
of which one has (2).
Solution. From (2), with no=4
Next: Trigonometric Integrals