Indefinite Integration of sec2 x

Indefinite Integration of sec^2 x

How to solve the indefinite integration of sec2 x problems: formula, example, and its solution.

Formula

(integral of sec^2 x dx) = tan x + C

∫ sec2 x dx = tan x + C

This is true because
[tan x + C]' = sec2 x.

Derivative of tan x

Example

Find the given indefinite integral. The integral of [(cos 2x) / (cos^2 x)] dx

cos 2A (Double-angle formula)

Split the fraction into two parts.

Change 1/(cos2 x) into sec2 x.

Trigonometric ratio - secant

∫ sec2 x dx = tan x

So (given) = 2x + tan x + C.