What's wrong with this solution of tan^3x?

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SUMMARY

The discussion centers on the integration of the function tan^3(x) and the confusion surrounding the correct answer. The correct solution is established as 1/2(tan(x))^2 - ln(sec(x)), derived from the identity tan^2(x) = sec^2(x) - 1, where the -1 is absorbed into the constant of integration. Participants clarify that despite different approaches, the results can converge to the same solution upon integration.

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I don't see what I am doing wrong in this. The answer I got is obviously not right. Appreciate any help. Thanks!
 

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Why is the answer you got obviously not right? I would say it is right.
 
Cause the answer is suppose to be 1/2(tanx)^2 -ln(secx)
 
so tanx^2 = secx^2 -1, and the -1 gets absorbed into the constant of integration.
 
Oh, yeah that would make sense. Is quite odd how two different things are exactly the same when you integrate them. Thanks.
 

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