### U-Substitution Integration on the TI-89: Raw Transcript

This is a video on u substitution with regard to e to the x

a transcendental function and a little more difficult one

which I wanted to show you of how my programs react to that

to get started were going to press second alpha

put the i n d e x letters in this entry line of the calculator

and then press alpha and put in the eight and the

open and closed parenthesis press enter and you’re into my menu

you can scroll up or down to many things here it’s really integration by parts that your

always thinking about when you do a transcendental cosign sign natural log or

e to the x if you’re going to integrate them you’d go to think integration by parts first

but we’re going to scroll up to e to the x here

choose e to the x from that menu and we’re going to enter the function

you have to press alpha before you enter anything in the entry lines of my programs

so alpha and we’re going to do five times x times e to the three times x

squared I always show you what you’ve entered

so you can change it if you’ve made a mistake or something

and I always ask you whether this if this didn’t equal each other then it would

not be u substitution so you need to tell me that

by stating yes or no it does equal, x equals x so were going to

press yes and then I explain to you that anything inside

the parenthesis of e to the x

the derivative must match the outside and so here’s our original function

we re write it anytime you have a number or a

constant inside the integral you always bring it out and put it on the outside of

the integral before you start to integrate

which I’ve done here you take what’s left the x

and put it over here in the x dx so thats re writing it

and I choose the u for you. here is the derivative of three x squared

it’s six x and then you always take here’s another thing where

there is a constant or number is outside or next to the x dx

you always put that on the other side make du one sixth du equals x dx

transpose it by division and then you do everything

all this on your test or homework whatever exactly correct exactly as you see it

here we’re multiplying the outside of the integral

times the du of the one sixth comes of du comes out side too

gives us five sixrths and then you substitute three x squared for

u answer

five sixths times e to the 3 x^2 plus c pretty neat huh

every stem calculus dot com go to my site, buy my programs

and pass calculus

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