   Chapter 7.1, Problem 14E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ x   cosh   a x   d x

To determine

To evaluate: The given integral using the technique of integration by parts.

Explanation

The technique of integration by parts comes in handy when the integrand involves product of two functions. It can be thought of as a rule corresponding to the product rule in differentiation.

Formula used:

The formula for integration by parts in terms of u and v is given by

udv=uvvdu

Given:

The integral, xcoshaxdx.

Calculation:

Make the choice for u and dv such that the resulting integration from the formula above is easier to integrate. Let

u=x      dv=coshaxdx

Then, the differentiation of u and antiderivative of dv will be

du=dx      v=1asinhax

Substitute for variables in the formula above to get

xcoshaxdx=x(1asinhax)(1a

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 5-8, graph the given function or equation. 2x3y=12

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 1124, find the indicated limits, if they exist. 14. limx3x3x+4

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Change 28 ft/s to ft/min.

Elementary Technical Mathematics 