Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Evaluate the indefinite integral as an infinite series.

$$\int x \cos \left(x^{3}\right) d x$$

$C+\sum_{0}^{\infty}(-1)^{n} \frac{x^{(6 n+2)}}{(6 n+2) \cdot(2 n) !}$

Calculus 2 / BC

Chapter 8

SERIES

Section 7

Taylor and Maclaurin Series

Sequences

Series

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

04:11

Evaluate the indefinite in…

02:37

02:05

04:22

Evaluate the integral.

03:36

03:20

02:12

01:24

Evaluate the indicated int…

02:51

07:21

Evaluate the integral.…

now on the same. What? I violate this, Uh, this is going by with this one, right? I wouldn't do it. Uh, with infinite Siri's, we already know that Cosa X with done it. Many, many, many, many times co signed X Here is negative one to the hand exit to input. Burn to n factorial. Right? Way we know this one. So we're gonna replace every instance of X with ex cubic. So Khoza x Q Whenever I see X, I'm gonna put eggs. Cute. So I see X here. I'm gonna put excuse So there's no excuse to end over two in factorial, which is just gonna be summation X to these six n So that is this one. Now what I want to buy expired those x you What am I gonna get? But it gets multiplication here, right? And so this is gonna affect this x year, right? So finally, is gonna be information negative one. That and there's gonna be exploited. Power six. And now when you multiply this by one eggs, this is the apparent one. When I combine it in most implication that I have to add the exponents, right? You wouldn't know this one. Eso this baby, uh, exited part of six and plus one or two in factorial right now, we need to find the integration, right. So they have to generate both sides. No. Is that simple? Right. So we find the integration, mind you in the integration, everything here that it's not X is gonna be like a is gonna behave like a constant. Right. So the integration is really gonna affect anything that is X, such as this one. Right? So that is just gonna be This is there's gonna be summation. We just might, Constance. Right. So we're just gonna see that's a constant because it doesn't contain an X. You're gonna have this over here to in here. Now the internet is running on him. I think this one right, cause you're doing it. DX. So what is the integral of this one? Well, integral of that one is gonna be, uh, X to the power six and plus one plus one. Right? Which is which is gonna be to right. This is gonna be except part of six n plus two over a six n plus two. Right? We just add one here, and it divided by it. The same thing, right? That is integration, remember? So why did you have that, then? This is gonna be summation. And from zero to infinity, Negative won t an extra powers six and plus two all over two and six and plus two. Now, this is just one form. You can put it. Uh, supposedly factorial a factory here. So this is this is supposed to be factorial. All right, so this is one we can put it. So So this estimation here is this guy right here.

View More Answers From This Book

Find Another Textbook

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

$$\int \frac…

$ \int \frac…

$$ \int x^2 …

Evaluate the integral.$$\int \cos ^{1 / 3} x \sin x d x$$

$ \int \sqrt…

$$\int \arct…

$$ \int \arc…

Evaluate the indicated integral.$$\int \sin ^{3} x \cos x d x$$

Evaluate the integral.$$\int \cos ^{2} 3 x d x$$

03:07

$19-21=$ Use the graphs of $x=f(t)$ and $y=g(t)$ to sketch theparametric…

06:47

Use series to approximate the definite integral to within the indicated accu…

01:35

Show that if $\lim _{n \rightarrow \infty} \sqrt[n]{\left|c_{n}\right|}=c,$ …

03:21

Suppose that the position of one particle at time $t$ is givenby$$\q…

02:18

Determine whether the series is convergent or divergent. If it is convergent…

03:43

$29-30=$ Use a graphing calculator or computer to reproducethe picture.<…

08:52

Find $$d y / d x$$$$x=1 / t, \quad y=\sqrt{t} e^{-t}$$

04:25

(a) Show that the parametric equations$$x=x_{1}+\left(x_{2}-x_{1}\right)…

05:20

(a) Approximate $f$ by a Taylor polynomial with degree $n$ at the number $a$…

02:42

$15-18=$ Describe the motion of a particle with position $(x, y)$as $t$ …

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.