Problem

Evaluate the indefinite integral as a power serie…

03:07

Problem 26 Easy Difficulty

Evaluate the indefinite integral as a power series. What is the radius of convergence?
$ \int \frac {t}{1 + t^3} dt $

Name: evaluate the indefinite integral as a power series what is the radius of convergence int frac t1 t3
Uploaded: 2018-03-08
Duration: 1 min 41 s
Channel: Numerade
Description: Evaluate the indefinite integral as a power series. What is the radius of convergence? $ \int \frac {t}{1 + t^3} dt $

Answer

$$\int \frac{t}{1+t^{3}} d t=C+\sum_{n=0}^{\infty} \frac{(-1)^{n} t^{3 n+2}}{3 n+2}$$

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Discussion

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Video Transcript

you value the indefinite in the girl as a power Siri's. And what is the readers of convergence? All right, so if we're going to expand these any girl as a power Siri's so we can just live t here and we expand one plus Team Cube. So that's going to be t to the power three end and from zero to infinity and the tea. So this's equivalent to signal. And from zero to infinity T departments three impasse won TT And here we require that cube It is apple. Less than one increases on minus one, which means the developed is less than one inch means or equals one. You release components. Lessees are all right. And here everything's changed, the other integral in summation drink us won tt So, uh, this is gonna be We're integral this part. So it becomes teaching our three M plus two overthrew impasse itude yet and our is equals to one. All right,

Yiming Z.

University of Illinois at Urbana-Champaign