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Problem 25 Easy Difficulty

Evaluate the indefinite integral as a power series. What is the radius of convergence?
$ \int \frac {t}{1 - t^8} dt $

Answer

$$C+\sum_{n=0}^{\infty} \frac{t^{8 n+2}}{8 n+2}, R=1$$

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Video Transcript

evaluate the indefinite integral as a power series. And what is the richest convergence? Okay, so the first gonna expanded as a power series, did he here? So this is tee times from zero to infinity to the power of Aden T T. And it goes to and from zero to infinity teaching power a or 18 plus one DT. We'll exchange the order of salmon Negro. So we're going to integrate these parts. Did he? And this is just so teacher power 18 plus 2/18 plus two. Yeah. So we have relegated indefinitely, grows as a power series, and one is really some convergence. So actually, we expanded for, uh, from this from this step. So this is step one and inquiries The absolute value of T two tower eighth is less than one. So that implies teas from 91 to 1. And the readers of convergence is r equals to one. Okay,

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