   Chapter 7.R, Problem 60E

Chapter
Section
Textbook Problem

# Verify Formula 62 in the Table of Integrals.

To determine

To verify:(duuna+bu)=a+bua(n1)un1b(2n3)2a(n1)duun1a+bu+C

Explanation

Formula Used: ddx(uv)=vu'uv'v2

Calculation:

We will verify the formula by using differentiation. To start with and for convenience, let F(u)=a+bua(n1)un1b(2n3)2a(n1)duun1a+bu+C and differentiate it with respect to u using the formula mentioned above.

F'(u)=1a(n1)×(un1)×b2a+bua+bu(n1)un2(un1)2b(2n3)2a(n1)1un1a+bu=un2a(n1)×ub2(a+bu)(n1)(un1)2

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