   Chapter 11.9, Problem 25E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral as a power series. What is the radius of convergence?25. ∫ t 1 − t 8   d t

To determine

To evaluate: The indefinite integral as a power series and radius of convergence

Explanation

Result used:

(1) The power series representation is 11x=n=0xn

(2) “The sum of the geometric series with initial term a and common ratio r is S=n=0arn=a1r .”

Given:

The indefinite integral is t1t8dt .

Calculation:

Let f(t)=t1t8dt .

By the result (1), consider the form 11x=n=0xn

Replace x for t in the result (2):

t1t8=t11(t8)=tn=0(t8)n=n=0t8n+1

Integrate the series,

(

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