   Chapter 8.5, Problem 33E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Integration by Parts In Exercises 33-38, use integration by parts to find the indefinite integral. ∫ x   cos   8 x   d x

To determine

To calculate: The integral of xcos8xdx.

Explanation

Given Information:

The provided integral is xcos8xdx.

Formula used:

Write the formula used in integration by parts method.

pqdx=pqdxp(qdx)dx

Here, p=p(x) and q=q(x)

Write the formula of integral of sinu.

sinudu=cosu+C

Write the formula of integral of cosu.

cosudu=sinu+C

Write the formula for derivative of un.

ddxun=nun1

Calculation:

Consider the provided integral,

xcos8xdx

Use the formula of integration by parts to find integral of above expression.

xcos8xdx=xcos8xdxddxx(cos8xdx)dx=xcos8xdx1(cos8xdx)dx

Here, p=x and q=cos8x

Multiply and divide by 8.

xcos8xdx=x8(cos8x)8dxI181((cos8x)8dx)dxII

Again, multiply and divide by 8 in part II

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