Calculus/Integration techniques/Reduction Formula

Integration techniques/Tangent Half Angle Integration techniques/Irrational Functions A reduction formula is one that enables us to solve an integral problem by reducing it to a problem of solving an easier integral problem, and then reducing that to the problem of solving an easier problem, and so on. For example, if we let Integration by parts allows us to simplify this to which is our desired reduction formula. Note that we stop at . Similarly, if we let then integration by parts lets us simplify this to Using the trigonometric identity, , we can now write {| | | |- | | |} Rearranging, we get Note that we stop at or 2 if is odd or even respectively. As in these two examples, integrating by parts when the integrand contains a power often results in a reduction formula. Integration techniques/Tangent Half Angle Integration techniques/Irrational Functions