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

Find the general indefinite integral.

$ \displaystyle \int \biggl( \frac{1 + r}{r} \biggr)^2 \, dr $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Gregory Higby

Numerade Educator

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

01:03

Frank Lin

00:49

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Campbell University

Oregon State University

Baylor University

Idaho State University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

0:00

Find the general indefinit…

01:40

01:18

Evaluate the integrals.

00:36

Evaluate the integrals…

01:48

02:29

Find the integrals.$\i…

00:37

Evaluate the integral.…

02:55

04:51

Evaluate the integrals usi…

03:31

the way I would do this. And enroll is just think about what it means to be uh something squared and you can just square each piece. So I'm just rewriting the problem the way it was written first like this and then off to the side. I'm thinking about doing some scratch work of what does it actually mean to be one plus R squared? What means multiplied by itself? So as you distribute each piece in there, I think it's pretty straightforward that you get 11 hour plus one hours to our plus R. Squared. And then the other thing is instead of just dividing everything by R squared in divide each piece by R squared. Um Because think about if you're dividing what you need the same denominator in order to combine them together. So I'm trying to just simplify this so that the inner role makes a lot more sense. Um This would be to over our, I like to leave it like that and you'll see why in a second. Plus one is when we go to take the derivative. So those are just some scratch work. Um You add one to your exponents and then multiply by the reciprocal through new experiment. Now this one if you were to leave this as ardent and then the first and add one, you would get to the zero and then you'd be divided by zero is undefined. So it makes sense then that there must be a different function that gives us that derivative and that answers to natural log about. And you can double check that's right. If you did a derivative of two natural log of our, you get that answer. The directive of that anti directive that is just are and don't forget about plus C. Um Now I would rewrite this. Just kind of out of habit like this and don't forget you need that plus C. Because uh the derivative of a constant zero and they're not going to write plus zero up here. So this is a good answer.

View More Answers From This Book

Find Another Textbook

01:30

Find the missing value of the probability distribution.X023<…

01:50

20.Using the Newton-Raphson Method with: @ (3 Points) f(r) 2x2 und po = 2 th…

02:35

QUESTION 4Consider you have been asked to run the follwoing hypothesis t…

03:35

Step 3; Restate the alpha level we ve chosen, and decide whether this is a o…

08:03

homogeneous system of two linear differential equations with constant coeffi…

00:29

Finding Classical Probabilities In Exercises 29-34,a probability experiment …

02:11

The following table represents the number of free throws a typical NBA playe…

01:10

Suppose we want to fom three-digit numbers using the set of digits {0,1,2,3…

03:54

Consider random variable X that is normally distributed. Complete parts (a) …