Powers of Tan and Secant

Jun 21st, 2015
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Alexandria Technical College
Course: mathematics
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Document is used by students for exam practice.

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Powers of Tan and Secant[edit]To 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 1[edit]Find .There is an even power of . Substituting gives soExample 2[edit]Find .Let so . ThenExample 3[edit]Find .The trick to do this is to multiply and divide by the same thing like this:Making the substitution so More trigonometric combinations[edit]For the integrals or or use the identitiesExample 1[edit]Find We can use the fact that , soNow use the oddness property of to simplifyAnd now we can integrateExample 2[edit]Find:.Using the identitiesThen

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