CK12 Calculus - Single Variable

Recallthat so by substitution,

The first integralshouldbe straightforward.The secondcan be doneby the methodof -substitutionby
letting so The integralbecomes

If and are both positiveintegers,then an integralof the form

can be evaluatedby one of the proceduresshownin the tablebelow, dependingon whether and are
odd or even.

Procedure Identities

odd Let

odd Let

and even Use identitiesto reducepowers

Example4:

Evaluate
Solution:

Here, is odd. So accordingto the secondprocedurein the tableabove,let so
Substituting,