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## Homework Statement

Evaluate the integral

integral of (tanx)^5*(secx)^4

## Homework Equations

## The Attempt at a Solution

what I did was broke the sec^4x into 2 sec^2's multiplied by each other

then one of these terms became tan^2x +1

so I had tan^5x*(tan^2x + 1)*sec^2x

then u = tanx

du = sec^2x

eventual answer tan^8x/8 + tan^6x/6 + c

however the book shows this problem by taking a (secxtanx) out of eveyrthing then doing tan^4x = (sec^2x -1)^2*sec^3x

u= secx

du = tanxsecx

eventual answer sec^8x/8 - sec^6x/3 + sec^4x/4 + C

...is there something wrong with the way I did it; I don't see anything wrong with the way I'm doing it but the book insists on doing all problems like this the otherway. I wouldn't mind but I don't like memorizing things and the way I always seem to think of doing these problems is the first method I wrote out please respond I have an exam on this stuff tomarrow night