# Integral Of Sinh(Ax)

Integral of sinh(ax) along with its formula and proof with examples. Also learn how to calculate integration of sinh(ax) with step by step examples.

Alan Walker-

Published on 2023-04-13

## Introduction to integral of sinh(ax)

In calculus, the integral is a fundamental concept that assigns numbers to functions to define displacement, area, volume, and all those functions that contain a combination of tiny elements. It is categorized into two parts, definite integral and indefinite integral. The process of integration calculates the integrals. This process is defined as finding an antiderivative of a function.

Integrals can handle almost all functions, such as trigonometric, algebraic, exponential, logarithmic, etc. This article will teach you what is integral to a trigonometric function sine. You will also understand how to compute sinh(ax) integral by using different integration techniques.

## What is the integral of sinh(ax)?

The integral of sinh(ax) is an antiderivative of sine function which is equal to cosh(ax)/a. It is also known as the reverse derivative of sine function which is a hyperbolic function. By definition, a hyperbolic function is a combination of two exponential functions e^x and e^-x. Mathematically, the sinh formula is;

$$\sinh ax=\frac{e^{ax}-e^{-ax}}{2}$$

### Integral of sinh(ax) formula

The formula of integral of sinh ax contains integral sign, coefficient of integration and the function as sine. It is denoted by ∫(sinh(ax))dx. In mathematical form, the integral of sinh(ax) is:

$∫\sinh(ax)dx = \frac{\cosh(ax)}{a}+c$

Where c is any constant involved, dx is the coefficient of integration and ∫ is the symbol of integral.