Correcting Integration of tan^5x: Differentiating and Verifying the Solution

[youmei0426]

Homework 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!

 

[Orodruin]

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

 

[Mark44]

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!