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

[Emethyst]

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 Any help would be greatly appreciated, thanks.

 

[Mark44]

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.

 

[Emethyst]

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.

 

[Mark44]

Yes, I misread what you wrote.