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You are here: Home / Archives for Natural Log

ln(2x) Integration by Parts

August 20, 2015 by Tommy Leave a Comment

Raw Transcript

This video is gonna be on integration with regards to natural log. It is very difficult to me, maybe no to you, but to me it’s very difficult. You never use it so it’s tough to come up with a test or homework. So it’s good to have a program like this. That’s why I programmed it myself. So let’s get started, 2nd alpha to enter formula to get to the menu, this tells you that you can enter letters in the titanium calculator. So we enter index 8 () and press enter. Scroll to integration by parts or if you wanted to find out about log of x. So I ask you in log of x, what do want to do? Differentiate, integrate or solve for x. Some tests have solving for x and log of x which is another tricky thing if you’re not used to it. That will be in another video. So we want to integrate, so we select integrate. We are in integration by parts, when you come to log of x and integrating we will do log or x which is In(x), select and put in the example. You should see: Evaluate a In(x) Integral Exmp: x^2* In(x) Remember to press alpha to enter the formula: x^2*In(x) ,then press enter. It shows what you are trying to integrate which should be: ∫[x^2*In(x)]dx, then select ok The function will appear as follows: ∫[x^2*In(x)]dx dv = (x^2)dx v = ∫[x^2]dx = x^3/3 u = in(x) du = (1/x)dx Notice I chose the dv which is already the derivative and v would be the integration of that. So dv is gonna be x^2. And v is the integral of x^2 which is gonna be x^3/3. For those of you who don’t know how that happened, I can’t do everything exactly step by step because we’re doing function of derivatives. In the integral of the x^2, you add 1 to the 2 (the exponent) and divide by 3, so we have x^3/3. When you divide by 3 you have to multiply times whatever is in front of the x and that’s 1 so it will be 1/3 times 1/3 or x^3/3. The u choice is going to be In(x), so the derivative of In9x) is (1/x)dx. Here is the function and the formula for integration by parts ∫[x^2*In(x)]dx = v*u – ∫[v*(du)]dx =x^3/3 [In(x)] • ∫[(x^3/3) (1/x)]dx = x^3*In(x)/3 • ∫[(x^2/3)]dx Further you can see =x^3*In9x)/3 • (1/3) ∫[(x^2)]dx =x^3*In(x)/3 • (1/3) (x^(2+1) / (2+1) = x^3 In(x)/3 =-(1/3) (x^3/3) We put the 1/3 in front of the integral sign and then integrate the inside. When you’re going to integrate x^2 notice I show you we’re going to do 2+1 add 1 to the exponent and divide by 2+1. So that’s exponent 3 divided by 3. The you have your answer for function ∫[x^2* In(x)]dx Answer = x^3*In(x)/3 -x^3/9+c Check my videos out on my website, eveystepcalculus.com and of course other videos that help you. You can purchase these programs and get through calculus very easily.

Filed Under: Integration, Natural Log

Natural Log ln(x) Solved for Test-Video

February 20, 2015 by Tommy Leave a Comment

Solve the Equation: ln(x+2)=3

Raw Transcripts
Hello, again. Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a, solve a natural log equation right no, on the Titanium. I’ll show you my program work on that. Index 8 to get to my menu. I’m already at the scroll down to log of x solved. Press enter and number three. Choose number three solving. You have to go through the menus. We’re going to enter the function. You have press Alpha before you enter anything into these entry lines, here. Alpha second log of X plus 2 equals 3. I always show you what you’ve entered, in programs, you can change in case you made a mistake. I say it’s okay. You’re going to multiply both sides by E. And when you multiply a log times E, you get X plus 2 simply. These are all simple but try to remember that during a test with the other any number of equations and rules you have to memorize to place into a calculus test. Pretty neat, huh? everystepcalculus.com. Go to my site, buy my programs if you want to pass calculus and subscribe so you can see more videos.Have a good one.

Filed Under: Calculus Help, Natural Log

Finding Natural Log Showing Work on TI89-Video

February 10, 2015 by Tommy Leave a Comment

What is the integral of ln(x^2+2*x) dx?

Raw Transcript

Hello, Tom from everystepcalculus.com and everystepphysics.com. We’re going to do a calculus problem with regard to natural log. And which we’re going to my menu here. Let’s do it. Index 8 to get to my menu. You can see the problem on your screen. And I’m already at log of X to save time here in the menu. But just scroll down from where it starts the A’s all the way down to L, here. Choose that. If you want to integrate a log of X. And we’re going to choose number two, Integration again. And we’re going to choose log a X, number one. And we’re going to enter the function. You have to press Alpha before you enter anything these entry lines here. Alpha second log, put the log in here. X squared plus two times X, close off the parentheses. I always show you’ve entered. You’ll notice that the calculator factored this. iIt always does that automatically which we need in this system of equations. So we’re gonna rewrite it and we’re going to put the one here because when you integrate one, you get X. So DV is one, V equals the integration of one and the answer is X. Which you need for the formula. Here’s the formula UV minus integral of V, etc.

 

Filed Under: Natural Log

Derivative of Natural Log on the TI89 | Every Step Calculus Video

October 14, 2013 by Tommy Leave a Comment

Raw Transcript

This is a video from everystepcalculus.com. Demonstrating how my program work on a ti 89 titanium calculator and other calculators in the ti system for physics and calculus problems now I’m going to demonstrate log problems ah with regard to my programs to enter the code to get into my menu you have to press second alpha and put i n d e x in here and then press alpha and the put the eight and the open and closed parenthesis press enter and you’re into my menu this is all alphabetical in my menu you scroll down to log problems in the l section there it is there and you have all these different things you can do with log problems right now I’m going to differentiate so I’m going to press number six you can scroll down or use the number here in the front I’m going to press number six give you the option of doing log to the base some other base or the natural log I’m going to do natural log first here and were going to enter our function you have to press alpha before you enter anything into the entry lines of my programs here your going to press alpha and then were gonna press second to enter the log function you have to add the ln there and let’s do it. six times x squared plus nine. I always show you it factored it here calculator did that automatically I always show you what you’ve entered so you can change it if you want I say it’s ok. And y is equal to log of some function in here f of x and here’s the function and the formula is y prime is equal to f prime of x divided by the function itself I show you the function. I show you the derivative of it taken the derivative and dividing it by the answer and ahh, the original function and her’s the answer four x divided by two x squared plus three. Pretty neat huh, everystepcalculus.com. Go to my site buy my programs and pass calculus.

Filed Under: Natural Log

Derivative of lnx | Natural Log on TI-89 | Every Step Calculus Video

October 14, 2013 by Tommy Leave a Comment

Raw Transcript

This is a video from EveryStepCalculus.com demonstrating how my programs work on a TI-89 Titanium calculator and other calculators in the TI system for physics and calculus problems. This is an example of finding the derivative of natural log in my calculus programs and let’s get started in my programs you have to push second alpha to put in the letters i n d e x and then press alpha to put the eight and the open closed parenthesis and press enter and you’re into my menu you’ll scroll down to log of x derivatives and you want to differentiate it so you choose that you can integrate it or solve for x also and we’re going to enter a function here you have to press alpha before you enter anything into my entry lines here So we press alpha. I’m going to press second and then log and let’s put in ah six times x squared plus seven. I always show you what you’ve entered so you can change it in case you made a mistake. I say it’s ok and we’re finding the derivative
of log of six x squared plus seven the formula is u prime over u u being what’s inside the parenthesis here
here is u here six x squared plus seven the derivative the derivative of that excuse me is twelve x and u prime over u so here’s the answer twelve x divided by six x squared plus seven ahh pretty easy if you know the formula and, but my programs show it step by step easily like this. Pretty neat, huh? EveryStepCalculus.com
go to my site buy my programs and pass calculus.

Filed Under: Natural Log Tagged With: lnx

Natural Log d/dx ln(x)

December 9, 2012 by Tommy Leave a Comment

Video Summary

How the calculus calculator (TI89) solves the Natural Log:
~ Bring up the menu and scroll to natural log
~ Enter functions by pressing alpha before
~ Enter your range
~ Program will review and ask for changes
~ It will substitute the lower limit of your function
~ It substitutes upper from lower and produces answer all step by step

Raw Transcript

This is a calculus calculator program or app for natural log functions with regards to solving for x in this video, using the ti-89 titanium calculator. To get to my main menu, you have to press second alpha and then the letters i n d e x again press alpha to enter the 8 and left and right parentheses. press Enter. And you’re into my menu. You have many many choices here. You also have logged at the base a, local max and mins means it’s graphing by hand. many many many choices e to the x derivatives, e to the x integrals, implicit differentiation, integration by parts. We’re gonna do natural log ln (x) today. And I give you the choice of differentiating natural log of x. Integrating or solving for x. We’re gonna solve for x today in this calculus calculator  program. And many tests they have this example here log within log of x. I’m going to do that now. Now you have to press alpha before you enter anything in my entry lines in my programs. Enter the log function within log of x. equals 7. I show you what your entered always. You can change it if you want. I say it’s okay. Multiply both sides by e and here’s the calculation. Use the approximate answer. pretty neat everystepcalculus.com Go to my site, pass calculus, enjoy my programs.

 

Filed Under: Natural Log Tagged With: Natural Log d/dx ln(x)

Natural Log Program

June 19, 2012 by Tommy Leave a Comment

Raw Transcript

This video is on natural log and the derivatives of that, or integrals depend on the choice, these are my fabulous programs that I’ve programmed under the titanium calculator that you can download from my website and do all these like you were an expert. I’m going to clear the entry line here by pressing clear and then I’m going to clear the screen by pressing F1 and 8, we need to enter index 8 in the home screen and I’m going to show you how to do that. Press second alpha, highlights that you are in the numbers or letter “1index* and then alpha 8 and close parenthesis which tell the calculator it’s a program and out comes my menu. You can see how many things are to do, you can scroll down this or whatever…area of a parallelogram, there is he chain rule, there cross product, all kinds of complicated stuff that you can do easily on this one, definite integral that’s always fun, it’s all alphabetical and then I give you a sheet if you buy the programs where you can see it on an 8 by 10 an outline of everything that’s on the calculator so it’s really easy to learn quickly and go to them. Anyway what are we doing? Oh we’re doing the natural log, there’s a natural log, in another video I did log to base A, they call it base a. So we are going to do the natural log right now and differentiate rather than integrate so I want to do those kind of problems and that’s what we’re into. I gave you the choice when you look at this menu because it’s one of the difficult things in calculus, certain for me was how to choose which problem to do but what function is necessary to do the problem; is it a chain rule problem, is it a product rule, is a quotient rule, is it U-substitution, what is it? Well and you pick out your problem and your test or homework and you say “oh gee, it look kind of like this number 3 here” you know that could be log of 5X cubed plus 6 or whatever in here and if it looks similar to that, we can press the number before that which I’ll do now and it tells you to that’s it’s U-substitution and now we are going to enter the function, so we’re going to press second and then log, here is the natural log function there, we are to press alpha and then we are going to enter our 5xX cubed plus 6 and so we are going to close the small screen so we’ll have to check it you know but it gives you the option of changing it if you did something wrong so you don’t worry about that, for instance I say it ok so we’re going to go on with it and you can see that here is the original function used in the inside your 5xX36 and U prime is which is the derivative of 15X squared. You
write this stuff on your paper to get 100% on this problem. Notice the U-substitution is U prime over U. so here is the U prime and here is the U and dividing it by the other heres 15 x squared plus that. Pretty neat huh. Ok everystepcalculus.com, check it out

Filed Under: Natural Log

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