# Integral of secx.tanx formula

## Formula

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

### Introduction

Take, $x$ as a variable, and represents an angle of a right triangle. The secant and tangent functions are written in terms of $x$ as $\sec{x}$ and $\tan{x}$ respectively. The indefinite integral of product of $\sec{x}$ and $\tan{x}$ functions with respect to $x$ is written in integral calculus as follows.

$\displaystyle \int{\sec{x}\tan{x} \,} dx$

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

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

#### Alternative forms

The indefinite integral of product of secant and tan functions formula can be written in terms of any variable in calculus.

$(1) \,\,\,$ $\displaystyle \int{\sec{(j)}\tan{(j)} \,}dj \,=\, \sec{(j)}+c$

$(2) \,\,\,$ $\displaystyle \int{\sec{(q)}\tan{(q)} \,}dq \,=\, \sec{(q)}+c$

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

### Proof

Learn how to derive the integration rule for the product of secant and tangent functions in integral calculus.

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