Is My Approach Correct? Solving the Integral of tan^4x-sec^4x

[mathnoobie]

I looked online and it gave a really simple method to solve it and it ended up with the solution
x-2tan(x)
I took a really weird approach and I'm not sure if my answer is right, and I'm hoping if someone could take the same approach and confirm if I did it correctly.
I basically separated the integral into 2 separate integrals and got a solution.
∫tan(^4)xdx-∫sec(^4)xdx

When I was done, I got the answer of
(tan(^3)x)/3-2tanx-x-(tan(^2)x)/2

 

[Bohrok]

You can always differentiate your answer and see if you get the original integrand.
However, the answer you got isn't equivalent to the answer x - 2tan x.

 

[DeIdeal]

You might want to try simplifying tan^4x-sec^4x first.