# Powers of Tan and Secant

Jun 21st, 2015
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Alexandria Technical College
Course: mathematics
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Powers of Tan and SecantTo evaluate .1. If is even and then substitute and use the identity .2. If and are both odd then substitute and use the identity .3. If is odd and is even then use the identity and apply a reduction formula to integrate , using the examples below to integrate when .Example 1Find .There is an even power of . Substituting gives soExample 2Find .Let so . ThenExample 3Find .The trick to do this is to multiply and divide by the same thing like this:Making the substitution so More trigonometric combinationsFor the integrals or or use the identitiesExample 1Find We can use the fact that , soNow use the oddness property of to simplifyAnd now we can integrateExample 2Find:.Using the identitiesThen

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