Quick Antiderivative of Tan^2x and Sec^2x

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Homework Help Overview

The problem involves finding the antiderivative of the function y=tan^2x+sec^2x, which falls under the subject area of calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to manipulate the expression by substituting tan^2 with sec^2-1 but expresses uncertainty about how to proceed further. Some participants provide hints related to derivative relationships, while others clarify the notation used in the problem statement.

Discussion Status

The discussion is active, with participants offering hints and clarifications. There is acknowledgment of a possible misunderstanding regarding the notation used in the problem, which has led to some confusion. Different interpretations of the expected answer have also been noted.

Contextual Notes

There is a mention of a potential mistake in the original problem statement regarding the notation of tan^2x and sec^2x, which may have contributed to the confusion in the discussion.

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Homework Statement


Find the antiderivative of y=tan^2x+sec^2x


Homework Equations


N/A



The Attempt at a Solution


Seems to be a simple question, but the answer is eluding me no matter what I do. My first try was to replace the tan^2 with sec^2-1, and then factor out a 1/2 from the resulting 2sec^2x-1, but after that I have no idea how to continue. I know that the answer I should wind up with is Y=2tanx-x+C, but have no idea how to go about getting this answer :-p Any help would be greatly appreciated, thanks.
 
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Hint: d/dx(tan(x)) = sec2(x)
Every derivative formula gives you an antiderivative formula for free, if look at it the right way.

I also believe the answer you should end up with is tan(2x) - x + C, which is slightly different from what you show.
 
Ohh I see it now, thanks Mark, and no the answer is correct, as it is what I arrived at as well just now.
It might have been my mistake writing the question wrong, as it is y=(tanx)^2+(secx)^2. I just wrote it as y=tan^2x+sec^2x assuming people would know that, for example, tan^2x=(tanx)^2. I apologize for that mistake.
 
Yes, I misread what you wrote.
 

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