   Chapter 6.2, Problem 6SWU ### 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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# In Exercises 5 and 6, use integration by parts to find the indefinite integral. ∫ 3 x 2 ln x   d x

To determine

To calculate: The indefinite integral 3x2lnxdx.

Explanation

Given Information:

The provided indefinite integral is 3x2lnxdx.

Formula used:

The rule of integrals by part:

[u(x)v(x)]dx=u(x)[v(x)]dx[ddxu(x)[v(x)]dx]dx

The derivative of function:

ddxxn=nxn1+C

Calculation:

Consider the indefinite integral:

3x2lnxdx

Now apply integration by part by considering lnx as first function 3x2 and second function,

[(lnx)(3x2)]dx=lnx[3x2]dx[ddx(lnx)[3x2]dx]dx

Now apply the deriv

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