Integral of [tan(2x) + sec(2x)]^2

[MarkSA]

Hello,

1) Find the integral of: [tan(2x) + sec(2x)]^2

I've given this one some thought but I can't see a way that would work. I don't think i can do u-substitution (at least not with it in this form)

I tried multiplying it out

tan(2x)^2 + 2sec(2x)tan(2x) + sec(2x)^2

But I can't do much with that either because of the squares.

Do you have any suggestions?

 

[o_O]

You can use the identity tan²x = sec²x - 1:

(sec²(2x) - 1) + 2tan(2x)sec(2x) + sec²(2x)
= 2sec²(2x) - 1 + 2tan(2x)sec(2x)

Now if you look at your trigonometric integrals, these expressions should look familiar.

 

[MarkSA]

Yes they do. Thank you