   Chapter 6.2, Problem 53E ### 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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# Finding Indefinite Integrals Using Two Methods In Exercises 51–54, find the indefinite integral (a) using the integration table in Appendix C and (b) using integration by parts. ∫ x 7 x − 3   d x

(a)

To determine

To calculate: The solution of indefinite integral x7x3dx using integration table in

Appendix C.

Explanation

Given Information:

The expression is provided as:

x7x3dx

Formula used:

The formula for the integral ua+budu is:

ua+budu=2(2abu)3b2a+bu+C

The general power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x.

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

du=dx

Consider the provided expression:

Consider the provided expression:

x7x3dx

Rewrite.

x7x3dx=x3+7xdx

Here, a=3, b=7, u=x and du=dx.

Substitute u for x, a for 3, b for 7, and du for dx

(b)

To determine

To calculate: The solution of indefinite integral x7x3dx using integration by parts.

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