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

## Sec^2x Integration Formula

The integration formula of sec^{2}x is given by

∫sec^{2}x dx = tanx +C

where C denotes an integral constant.

## What is the Integration of sec^2x

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

*Proof:*

First, recall the function whose derivative is the function sec^{2}x. We know that the derivative of tanx is equal to sec^{2}x, that is,

$\dfrac{d}{dx}$(tan x) = sec^{2}x.

Integrating both sides, we get

∫$\dfrac{d}{dx}$(tan x) = ∫sec^{2}x dx +K, K is an integral constant.

⇒ tan x = ∫sec^{2}x dx +K

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

⇒ ∫sec^{2}x dx = tanx -K

⇒ ∫sec^{2}x dx = tanx +C where C=-K.

So the integration of sec^{2}x (sec square x) is equal to tanx+C where C is an arbitrary constant of integration.

**Related Derivatives:**

Integration of sin^{2}x | Integration of sin^{3}x |

Integration of cos^{2}x | Integration of cot^{2}x |

Integration of tan^{2}x | Integration of tanx |

## FAQs

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

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