Find a power series representation for the function. (Give your power series representation centered at x = 0.) g(x) = x5 In(1+x) g(x) = n = 1 X Evaluate the indefinite integral as a power series. 1 f(x) = c + [x³11 x5 In(1 + x) dx 00 2( Σ n=1 What is the radius of convergence R? R = 1

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.4: Improper Integrals
Problem 13E
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Find a power series representation for the function. (Give your power series representation centered at x = 0.)
g(x) = x5 In(1 + x)
g(x) = Σ 1
n = 1
X
Evaluate the indefinite integral as a power series.
[x³1
x5 In(1 + x) dx
Σ(
n = 1
What is the radius of convergence R?
R = 1
f(x) = C +
Transcribed Image Text:Find a power series representation for the function. (Give your power series representation centered at x = 0.) g(x) = x5 In(1 + x) g(x) = Σ 1 n = 1 X Evaluate the indefinite integral as a power series. [x³1 x5 In(1 + x) dx Σ( n = 1 What is the radius of convergence R? R = 1 f(x) = C +
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