Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Evaluate the integral.

$ \displaystyle \int \frac{x^2}{x^6 + 3x^3 + 2}\ dx $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by J Hardin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

09:28

02:41

08:10

03:13

Evaluate the integral.…

02:17

Evaluate the given integra…

04:06

05:02

07:28

04:49

01:43

Evaluate the integrals.

Let's start off here with the use of Let's take you to be x cubed, then do you? Over three is X square D X and that's exactly what we see in the numerator over here. X squared dx. So also, we have to rewrite this exit six is X cubed square so that you square so on the bottom. Let's do the denominator first. Excellent. Six three x cubed plus two in on the top where he saw that this is just do you and then we have to divide by the three Let's pull off the one third. So now this is a much better looking at a girl because weaken factor that denominator And then we could do partial fraction to composition here. So in this case, you want to find numbers and be such that we can rewrite the immigrant to be this, and it turns out that we have b who's won. So we have won over you, plus one and then we have a is minus one. All right, so use partial fraction the composition match up the coefficients to find your A and B as we did in the previous section. God and evaluate thes. That's a three out there, plus one minus. It's one thing I heard and then plus two. So here I just distributed the one third and generated both of these. I added that constancy of integration. So here we could do two steps. So pull out the winter and then I rewrite the longer of them as a fraction because its attraction and then I just replace you with execute. So on top of you, plus one so X cubed, plus one and then on the bottom X cubed, plus two. And then let's add in our constant of integration, see? And there's our final answer.

View More Answers From This Book

Find Another Textbook

02:37

Q1:An insurance company selected samples of clients under 18 years of ag…

00:19

A probability model for a binary dependent variable is only plausible if its…

05:45

CCdU.otof 27 (3 complete)Instructor-created question The followi…

10:26

The revenue R (in dollars) from renting apartments can be modeled byR = …

02:29

Poisson Classifier for Multiclass Classification. Let X € R be uivariate ran…

05:58

D Learning Task 1 JG L Simplify by writing in exponential form 2(21(21(21(21…

08:12

A school has 650 pupils of which 300 are boys . Represent the ratio of girls…

01:28

4) Convert the following logarithm expression to exponential form:log5 2…

04:15

9 ? % 8 8 8 8 - % 8-95 ? 2 82 < A 81

01:59

13) Given the total revenue R(x) = 30x and the total cost C(x) = 0.5x? Sx+ 2…