   Chapter 8.3, Problem 11E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral Involving Sine and Cosine In Exercises 1–12, find the indefinite integral. ∫ x sin 2 x d x

To determine

To calculate: The value of integral using by-parts xsin2xdx.

Explanation

Given:

The provided expression is xsin2xdx.

Formula used:

The by-parts rule is udv=uvvdu.

The trigonometric rule is sin2u=1cos2u2.

The cosine rule is cosudv=sinu+C.

The sine rule is sinudv=cosu+C.

Calculation:

Consider the function xsin2xdx. …… (1)

Let u=x,dv=sin2xdx

Solve both separately.

First,

u=x …… (2)

Differentiate both sides

du=dx …… (3)

Now solve the other one.

dv=sin2xdx …… (4)

Integrate both sides,

Recall the trigonometric rule is sin2u=1cos2u2.

v=1cos2x2dx

Simplify

v=x2sin2x4 …… (5)

Recall the by-parts rule udv=uvvdu

### 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

#### Find more solutions based on key concepts 