MrieonomctFIC substitution_Ys- Eelueto know, this integral cn 21so following integral Ming K= TRIGONOMETRIC Dloze by u-sub (s0 n2 next) . BUBSTITUTION_ Howover, do ...

Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable.
$$\int \frac{\theta^{3} d \theta}{\sqrt{9-\theta^{2}}} d \theta$$

In the problem we have integral cost a to D. T. Dot a bomb sign squad tita Last two. Sine Theta -3. Now here we assume you equal Scientific. So do you equal costly to the T. To? Hence in addition can return us. Do you work on You a Squire plus do you -3? No this can be represented as one upon you plus three. Do you -1 equals f. On you? Plus three Plus be upon your -1. So for the solving we obtained the value of A. Has- went up on four B equals Went up on four. And This integration become -1 upon four. Digital. Do you upon you plus three Plus one upon 4 duration. Do you upon U -1 equals minus one upon four. Helen mod You plus three Plus one upon 4. Ellen mode U -1 Plus C. Therefore it is equal to minus one upon four. Ellen mud Scientific a Plus three Plus one upon food. Ellen meara Scientific A -1 Last See. Or this is equal to -1 upon four. Ellen morgan Scientific A plus three Fun Scientific A -1 class C. So this is the answer.

This question tells us to evaluate the integral by making the given substitution. As you can see, they've told us to make the substitution that you was co sign of data. Therefore, negative D'You is signed. Data defeat a duck's remember the derivative of coastline is negative sign which gives us negative you to the fourth because we're increasing exploded by one dividing by the new exponents And now we're back substituting in instead of you It should be negative. Co signed the fourth of data divide by four plus C.

We have in addition, cause you to die. The sign T uh, digital you. It was caused, Tita. I knew it was minus sign. Tita. Daisy. So does he. Wonder my ass. And ago you have about three day. It is equal to minus. You did about for over full. Let's see villages, even as minus one of four. Got our full TJ. Let's see. This is dancer.

So be solved here. The goal, of course, is cubic square. Did a fight about spur there? So I want to do this using the production. We don't know. However, it in the form it is currently can't use those because we discovered that a crew can't Operator? Yes, a practice where they that in the denominator. And this car is a problem for us. Uh, would you change this before unify our performance? So to do this won't just your simple new substitution. And we will let you. You Teoh square with Nina. You hear this very theater. So do you. You see 2 1/2 squared. You think so? Rearranging this in terms. To isolate data, you have to to square a theater. You so we can play this into working here. So we now begin to grow Cosi cute of you over scribbler times two square root of you. So we get a cancellation here. This is a non here. You can pull this two x factor too. Right here to the funds. What we're left with is to integral, of course isn't cubed. Do you? Now there is a reduction continent that applies to this although it doesn't quite look like it's in this form is a different form of just one over sign that you that's flexible. We have BST How's he can't u is equal to one over sign you So they were not formula that we're going to use it looks like this. Let's use extra now That's how you normally but integral the X over Sign Our end of a X constant is equal to negative one over and minus one. Nice. How sign of the X. Divided by sine the power and minus one. But the X US and minus two over and minus one ties the same thing, nor has seen that formula except instead of signed with power. And we didn't have sign to the power and minus two, the X So we confine this to our formula here. Khost is because this is equal to into one over science. Cute. You you you hear. So in this case we have in you call the three more A is equal to one That's just one times you this you So you apply this to our equation just like to your arrest this line to make some room so we now? God, you and your fellow do you? Over. Sign Cute. You We have to. Is you two guys? Negative. One over three, minus one that dispenses with three. That's co sign you over. Sign to the power to you. Plus three minus two over three, minus one. That's integral. It's very you over Sign, have you? No. In this case, it's signed with power one because it's through my eyes to one. So you have this beautiful. Now the whole lot site here has been solved that we don't need to do anything more. What would you have this integral to solve? So start off problem. We'll just do a little bit of rearranging. Simple. Fine. So this factor right here three minus one is to so one over to what happened. So I cancel witness to And this over here three minus ones. Three wise to one's right through once ones too. So we have over two. So that will also cancel with this too. So what we're left with is negative. Cool. Sign you and I'll bring this science square into the numerator, Jr D Costa. That was so we have cause I knew times. Cool ck square of you. Us. Did you go? Uh, who's he? Can't you? You So we cannot solve this much more easily Because this is a common in tickle that we know from our integral tables. And we know the people. You, you you a natural rhythm. You can you aren't you Plus c So what? This into our formula, Our solution or with this church here? Oh, yeah, This negative hosting you I was cool. C can't swear you plus national I agree you can of you over to plus c almost like to do now is playing our former back into this woman back substitution. So we have negative co sign of the square. Earthy. That was cool. Seek and square the square here. Us the natural light room. Yeah. In this square data over to plus C. That is the final solution. Question