Hello, Tom from everystepcalculus.com and everystepphysics.com. We’re gonna do a problem in calculus regarding integration by parts. Okay, I’m gonna do a series of these because that’s what I’m working on right now or cleaning it up whatever. Answering more problems for people this is once answer was given by a student for Yahoo, integrate Y equals X times E to the 2X. How do I do this does E stay the same I mean these are common questions are you gonna integrate that okay. Well, because it’s E to the X you know that you know you have to learn something in calculus you’re gonna say that’s integration by parts anytime you’re this called a transcendental functioning. So, you have to integrate that with the integration by parts you know so, I’m gonna show you how to do that index 8 to get to my menu. I’m already adding integrate by parts I’ll pull it up here so you can see it integrate by parts. Okay, so that’s what you choose and we’re gonna press enter and we’re gonna choose E to the X here okay. You’re going to scroll to that I’m going to scroll up to that you can press the number in front of it if you want I mean that’s quicker. I’ll do that I’m going to press number two we’re going to integrate some form of E to the X there is E to the X okay.
Now, I’ve already entered the problem here so for quickness and so the simulator doesn’t screw up on me but I’m gonna show you I’m gonna press number two here and go back for you to do it you press alpha first before you enter anything in here. Alpha you’d go X and then X and then this yellow button here and then the X which is the E portion of it. E to the two times X and close off the parenthesis on the right and here’s what you’d have right here okay and we’re gonna say it’s one okay. So, here’s what we do here’s the problem we go U equals x which is out here, D U is equal to a derivative of that which is 1DX okay and then DV is E to the 2X and we’re trying to get the V answer. Which is the integral of the DV with respect to X which turns out to be E to the 2x divided by 2 okay. Write this on your paper just exactly like this okay, the formula for that for integration by parts is UV minus the integral of VDU and so we’re going to add what we just found here. U is X ok times V which is E to the 2x divided by 2 minus the integral of E to the 2x my divided by 2 times the derivative of that which is D U which is 1DX okay and then we clean it up I multiply it together clean up this and here’s what we end up there okay.
So, now we’re gonna do this integral here and when we do the integral it becomes minus E to the 2x divided by 4 plus C. Anytime you do an integration it’s got plus C unless it’s a definite integral where you have a certain range to it and so then where’d we have to distribute the minus sign here. Which I do so it’s plus a minus E to the 2x divided by four now the trick here factor out E to the 2x, if we factor out E to the 2x we get 2x minus 1 times e to the 2x divided by 4 plus C. Which is the answer pretty neat huh go to my site buy my programs and enjoy passing calculus they’re only 40 bucks, well worth the money you’ll have it for the rest of your life in your calculator. You can do calculus like I can do it for the rest of your life where you couldn’t no matter how many books you have in your bookshelf or notes from your professor remember these are null notes from me. In other words once I do a problem and figure out how the step by steps go these are my notes. This is my notes and so you can bring this into any test and you’re gonna pass that test with calculus okay. So. think about that no big deal. Hey, go to my site buy my program and pass calculus. Have a good one.