The given is:

$\displaystyle \int\frac{tan^2 e^{-x}}{e^x}dx

$

and the answer is:

$\displaystyle -tan e^{-x} + e^{-x} + c$

MY answer is:

$\displaystyle -tan e^{-x}+ c$ yeah, I know I'm wrong

So, can someone explain how did my book got that second term($\displaystyle e^{-x}$)?

If you rewrite the original given it would be,

-$\displaystyle \int sec^{2}-1 u du$

So where did it get the second term?

thanks