Integration of sec square x | Integral of sec^2x

The integration of sec square x (sec2x) is equal to tanx+C. In this post, we learn how to integrate sec^2x.

Sec^2x Integration Formula

The integration formula of sec2x is given by

∫sec2x dx = tanx +C

where C denotes an integral constant.

Integration of sec^2x

What is the Integration of sec^2x

Answer: The integration of sec^2x is tanx+C.


First, recall the function whose derivative is the function sec2x. We know that the derivative of tanx is equal to sec2x, that is,

$\dfrac{d}{dx}$(tan x) = sec2x.

Integrating both sides, we get

∫$\dfrac{d}{dx}$(tan x) = ∫sec2x dx +K, K is an integral constant.

⇒ tan x = ∫sec2x dx +K

[this is because the integration is the opposite process of derivatives]

⇒ ∫sec2x dx = tanx -K

⇒ ∫sec2x dx = tanx +C where C=-K.

So the integration of sec2x (sec square x) is equal to tanx+C where C is an arbitrary constant of integration.

Related Derivatives:

Integration of sin2xIntegration of sin3x
Integration of cos2xIntegration of cot2x
Integration of tan2xIntegration of tanx


Q1: What is the integration of sec^2x?

Answer: The integration of sec^2x is given as follows: sec2x dx = tanx +C where C is a constant.

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