# Integration problem of tan^5x

#### youmei0426

Problem Statement
find the integration of (tanx)^5
Relevant Equations
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This is my working out, and I also included the correct answer in the last line. The answer used a different method, however, what did I do wrong with my method? Thanks for the help!

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#### Orodruin

Staff Emeritus
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$1 = \cos^2(x) + \sin^2(x)$

#### Mark44

Mentor
This is my working out, and I also included the correct answer in the last line. The answer used a different method, however, what did I do wrong with my method?
Your answer is also correct. You can verify that your answer is correct by differentiating it, which should result in the original integrand.

You should write your answer as $\frac 1 4 \sec^4(x) - \sec^2(x) - \ln|\cos(x)| + C$
If you use the identity $\sec^2(x) = \tan^2(x) + 1$ on your answer, you should see that your answer and the posted answer differ only by a constant.

#### youmei0426

Your answer is also correct. You can verify that your answer is correct by differentiating it, which should result in the original integrand.

You should write your answer as $\frac 1 4 \sec^4(x) - \sec^2(x) - \ln|\cos(x)| + C$
If you use the identity $\sec^2(x) = \tan^2(x) + 1$ on your answer, you should see that your answer and the posted answer differ only by a constant.
Aah i see now, thanks a lot!

"Integration problem of tan^5x"

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