Question

Use substitution to evaluate the integral sec^2(x+2)dx

Answer 1

sec^2 is the derivative of which trig function?

Answer 2

tan right?

Answer 3

right, so the antiderivative of sec^2(u) is...?

Answer 4

tan(u)

Answer 5

so x+2 is u?

Answer 6

yes
you can check that the 2 doesn't change anything by doing the following:
u=x+2
du=dx
hence this is the same as
sec^2(u)du

note this would not be quite the same if it were something like sec^2(2x+2), as I'm sure you'll be dealing with shortly

Answer 7

okay, I just never know what to put as the U haha. Thank you!

Answer 8

welcome, you'll be getting plenty of practice with u's soon enough