Problem

Use series to approximate the definite integral t…

02:50

Problem 56 Hard Difficulty

Evaluate the indefinite integral as an infinite series.

$$ \int \arctan (x^2) dx $$

Answer

$\sum_{k=1}^{\infty} \frac{(-1)^{k-1}}{(2 k-1) !} \frac{x^{4 k-1}}{4 k-1}$ where $c$ is a constant

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Discussion

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Problem 56

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Video Transcript

so evaluated in that on any girl as a mysterious Okay, So I'm going first, expand our kind of a square, and this is equals to signal X squared to power on Took a menace one over to Korea. Tom's was one hell of a K minds one case from once. We've already Yes. So we're just right in here to make everything clear. This is equals to Xmas. That's Cuba with rhetorical us. Except for the fact the fact Victoria minus extra seven network sent Victorio and Yeah, we change X to X square. So long itching is correspondingly the his terms. Okay, So, uh, all right. And we're gonna interchange the grow. And so from one you know, anyone this part. So in the end, it's gonna be extra power of two came One is for the X. Yeah, and this is equals to So the result for our integration This is just extra core of four K minus one. A war for community. And this is our final results as the event the world in that any girl as a miniseries

Yiming Z.

University of Illinois at Urbana-Champaign

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Problem

Use series to approximate the definite integral t…

Problem 56 Hard Difficulty

Evaluate the indefinite integral as an infinite series.

$$ \int \arctan (x^2) dx $$

Answer

$\sum_{k=1}^{\infty} \frac{(-1)^{k-1}}{(2 k-1) !} \frac{x^{4 k-1}}{4 k-1}$ where $c$ is a constant

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Catherine R.

Heather Z.

Kayleah T.

Samuel H.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 11

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Catherine R.

Kayleah T.

Caleb E.

Michael J.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Problem

Use series to approximate the definite integral t…

Problem 56 Hard Difficulty

Evaluate the indefinite integral as an infinite series. $$ \int \arctan (x^2) dx $$

Answer

$\sum_{k=1}^{\infty} \frac{(-1)^{k-1}}{(2 k-1) !} \frac{x^{4 k-1}}{4 k-1}$ where $c$ is a constant

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Catherine R.

Heather Z.

Kayleah T.

Samuel H.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 11

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Catherine R.

Kayleah T.

Caleb E.

Michael J.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Evaluate the indefinite integral as an infinite series.

$$ \int \arctan (x^2) dx $$