Question

integrate sec^2 (2t) dt

Answer 1

help!

Answer 2

Use u-substitution for 2t.
u = 2t
du = 2dt
du/2 = dt

hence, your integral is \[\frac{ 1 }{ 2 } \int\limits \sec^2(u)du = \]
You should recognize the trig integral of this trig function. You should have it memorized. it's one of the basic integrals.
you can prove it, but I think it's faster for future reference if you just learn it.

Answer 3

next:
remember that, \[\frac{d(\tan u)}{du} = \sec^2 u\]
then you can solve it easily :)