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Prove the Reduction Forumla

1. Homework Statement
a)Prove the reduction formula:

[tex]\int\ tan^n\ x\ dx\ =\ \frac{1}{n-1}tan^{n-1}\ x\ -\int\ tan^{n-2}\ x\ dx[/tex]

Hint: first write [tex]tan^n x[/tex] as [tex]tan^{n-2} \ x\ tan^2\ x[/tex] and the rewrite using [tex]tan^2\ x+1=sec^2\ x[/tex].

b) Use the formula twice to find [tex]\int\ tan^4\ dx[/tex]

3. The Attempt at a Solution

I not sure what they're asking for when they say "prove". How should I begin with this one? Thanks
 

Answers and Replies

Vid
401
0
Use methods of integration to show the left side equals the right. From the form of the right side, it should be pretty obvious which method to use.
 

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