   Chapter 6, Problem 6TYS ### 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 5–7, use the integration table in Appendix C to find the indefinite integral. ∫ 3 x 2 1 + e x 3   d x

To determine

To calculate: The value of indefinite integral 3x21+ex3dx.

Explanation

Given Information:

The integral is provided as:

3x21+ex3dx

Formula used:

The formula for integral 11+eudu is:

11+eudu=uln(1+eu)+C

General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x3.

Differentiate the considered function with respect to x using power rule of differentiation.

du=3x2dx

Consider the provided integral:

3x21+ex3dx

Rewrite.

3x21+ex3dx=11+ex33x2dx

Substitute u for x3, and du for 3x2dx

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