Hello. Tom from everystepcalculus.com and everystepphysics.com. A step-by-step process for solving an e to the x problem. Transcendental problem. Normally in my programs, if you see a cosine or sine sign and you’re integrating those and log, and e to the x, you are thinking about integration by parts, ok. But I checked for you so you go to integration by parts you and you put the those things in there and and I find out if it’s u substitution or integration by parts and then I’ll direct you in those direction or solve it that way. So, let’s do it. Index 8 to get to my menu. Scroll down to integration by parts because they’re asking this on the test program or homework problem. And integrate by parts here and of course, these are the choices here. You’re going to choose number two, e to the x and we’re gonna add our
function. You have to press alpha before you enter anything in this entry lines here. Alpha x times e to the 3 times x squared. Keep in mind the integral of e to the 3 x squared or e to the 3 x cubed, etc. This can be solved because of one of the tricks in calculus. And it can be solved because because the inside the parentheses, the derivative of this matches the outside and I’ll show you how to do that. You need to know their derivatives right away in calculus you or you’ll never get through calculus. For instance, you look at this and say the parentheses, you’re going to come up with 6x right away, not even a question about it. And 6x is close and x on the outside here so I’ll show you how to do that. Any time you enter a problem, I show you what you’ve entered, you can change it if you want. I say it’s ok. I ask you this because I’m checking whether the inside of the derivative matches the outside. In this case it does so we’re going to answer yes. This is a u substitution problem and it goes to another program u substitution so I asked you the question again no big deal we can do these things to get through our tests and homework, get through calculus. Say it’s yes and then we solved the problem. We rewrite u substitution to make it easier for instance, I took the x and put it over xdx. See it here. That’s what we’re going to match. And this is one of the big clean tricks that I’ve learned in my programs how I tell people like yourself to do the problem. U equals 3 x squared, DU equals 6x dx , you gotta take the 6 and move it over here to make the ex dx to match the problem that we just showed you in the previous screen. And then we go into you can change the u parameters. We did. The integral of e to the u is actually e to the u. That’s the reason they use it so much in calculus tests and such is because it looks complicated and it is complicated unless you know that trick. So here is the answer, 1 sixth, notice we we had e to the u with du divided by 6, you always the constants out of the integral. I just do one because it can be more complicated when we do it then 1, 10, 15 whatever. I do that for you here, too. And here’s the 1 sixth times e to the u and then we substitute back to get this. Pretty need, huh? everystepcalculus.com. Go to my site, buy my programs and pass calculus. Best deal you’ll ever make. Believe me you’ll never throw it out. You’ll throw your calculus book but you’ll never throw these programs within your titanium out. Have a good one. I’m all for you passing calculus.