antiderivative of (sec(x))^2?

3 ⤊

what is the antiderivative of this? help please?

2007-08-22 09:14:38 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

∫sec^2(x) dx = tan(x) + c

Derivative of tan(x) = sec^2(x).
So, the anti-derivative of sec^2(x) = tan(x) + c

2007-08-22 09:19:13 · answer #1 · answered by Anonymous · 2⤊ 0⤋

Since d/dx(tan x) = (sec(x))^2, the antiderivative of (sec(x))^2 = tan(x) + c
You have to learn the basic differentiation formulas "backwards".

2007-08-22 16:20:12 · answer #2 · answered by hemidemisemiquaver 2 · 0⤊ 0⤋

That's a basic elementary form. The answer is tan x + C.

2007-08-22 16:46:15 · answer #3 · answered by steiner1745 7 · 1⤊ 0⤋

sec(x) ^2

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

use identities

2007-08-22 16:19:02 · answer #4 · answered by Anonymous · 0⤊ 2⤋