Math Doubts

Integral of sec²x formula

Formula

$\displaystyle \int{\sec^2{x} \,}dx \,=\, \tan{x}+c$

Introduction

Assume, $x$ is a variable, which is also used to represent an angle of a right triangle. Now, the square of the secant of angle $x$ is written as $\sec^2{x}$ and the indefinite integral of $\sec^2{x}$ function with respect to $x$ is written in the following mathematical form in integral calculus.

$\displaystyle \int{\sec^2{x} \,} dx$

The integration of secant squared of angle $x$ function with respect to $x$ is equal to sum of the tan of angle $x$ and the constant of integration.

$\displaystyle \int{\sec^2{x} \,}dx \,=\, \tan{x}+c$

Alternative forms

The integral of secant squared function formula can be written in terms of any variable.

$(1) \,\,\,$ $\displaystyle \int{\sec^2{(l)} \,} dl \,=\, \tan{(l)}+c$

$(2) \,\,\,$ $\displaystyle \int{\sec^2{(p)} \,} dp \,=\, \tan{(p)}+c$

$(3) \,\,\,$ $\displaystyle \int{\sec^2{(y)} \,} dy \,=\, \tan{(y)}+c$

Proof

Learn how to derive the integration of secant squared function rule in integral calculus.

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved