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.



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