Mathegoras

How to integrate sec(x)

Published On :2020-12-20 22:22:00

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\int s e c x d x

Multiply the integral by

\frac{s e c x + \tan x}{s e c x + \tan x}

\int s e c x . \frac{s e c x + \tan x}{s e c x + \tan x} d x

\int \frac{s e c^{2} x + s e c x \tan x}{s e c x + \tan x} d x

Now derive

sec x+tanx

It will equal

s e c^{2} x + s e c x \tan x

This is the formula of the denominator

The solution for the integral will equal

\int s e c x d x = \ln (|s e c x + \tan x|)

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