HOW WOULD YOU integrate this equation between zero and pi/2

Question

1/(1+(tan^2008)xdx

Answer 1

let u = 2008 x.
Then the integrand becomes
(1/2008)* 1/(1 + tan^2 u) du
= (1/2008)sec^2 u du
The limits of the u integration are 0 to 1004 pi

The integral of sec^x u is tan u

So I get the answer to be (1/2008) tan (1004 pi)
Since 1004 pi is an integer-multiple of 2 pi, the answer is zero.

Check my thinking

Answer 2

I meant to write
The integral of sec^2 u is tan u
The other steps are OK, I believe