   Chapter 4.5, Problem 16E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. ∫ sin x x d x

To determine

To evaluate:

The indefiniteintegral sinxxdx

Explanation

1) Concept:

i) The substitution rule

If u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then f(gx)g'xdx=f(u)du.

ii) Indefinite integral

sinx dx=-cosx+C

2) Given:

sinxxdx

3) Calculation:

Here, use the substitution method because the differential of the function x is 12xdx

Substitute u=x.

Differentiate u=x with respect to x.

du=12xdx

As dxx is a part of the integration, solve for dxx by multiplying both side by 2

### 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

#### Convert the expressions in Exercises 6584 to power form. 3

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 14, find the values of x that satisfy the inequality (inequalities). 1. x + 3 2x + 9

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

#### ∫(x − cos x)dx = 1 − sin x + C 1 + sin x + C

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 