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Evaluate the following integral: dx +C cVr2 = 9 Note that an arbitrary constant has been added for you....

Question

Evaluate the following integral: dx +C cVr2 = 9 Note that an arbitrary constant has been added for you.

Evaluate the following integral: dx +C cVr2 = 9 Note that an arbitrary constant has been added for you.



Answers

Evaluate the indefinite integral.
$\int(9 x+2) d x$

In this question we have to integrate the given function that is acts by access where plus nine to integrate it. I am going to make a substitution that use it was to access where plus nine it's a derivative is doing it was to to work cdX It shows that accidents should be replaced. Why do you want to so make the substitutions in the integration? You have such a huge tax. R d x Y. When do you know what you do? And in the denominator you got here to you. Okay now you can see that one but with the constant take it outside of the integration and we simply remain with we want to warn you, do you? No integration of one upon you is very simple. I can say that Ellen off more you Let's see this is the integration here and now we have to there is substitute the value of the new year After this. A tradition we can see that we got here one x 2. I learned more. Loss of access were Plus nine. Let's see. This is the answer for the given question here. And you can also right here. Models Okay. And you can also remove here more or less because there is a positive number and we Mhm. Don't be here more or less. Okay. So we can see that you can write both the forms here. Okay? Thank you.

Indefinite in terms and I x Quentin X noticed under constant camping outside Then we can have a night into girl on the next quiet D X and re condom the power role. Here, get any coaching expert and this one off. And this one has a constancy. No forgetting which been night times? No. This one being that expelling three over tree press A constancy in recently five getting cartoon, uh three Experiment three class A constant C.

All right. I'm going to use U substitution to explain this problem. I know a lot of students would be good and just guessing and checking. Um And I would trust my students to do that. So you might fall into that category. But using U substitution, the trick is to let U equal the denominator because then do you? Well the derivative of 50 So don't write that down. The derivative of negative four X. Will be negative four dx. And what I typically do is I saw for dx by dividing that negative four to the left side. So negative 1/4 to you. So that would give me a new integral. And I usually leave that nine alone replace that five minus four X with you because that's what I said is equal to and then D. X. Is equal to this dx I should clarify is equal to negative 1/4 times. Do you? So when I go to rewrite that problem now I would move that negative nine force in front. Because of positive times a negative is negative. And you can move constants that are multiplied in front of an integral because now I can take that integral. Um that negative nine forces still there natural log of the absolute value of. You don't forget about your plus C. Have to have a plus C. With an indefinite integral. But then remember we we started with excess. We need to end with excess. And so that's a negative nine force. Natural log we let U equal five minus four X. I shouldn't have tried to squeeze it right here plus C. And there's your final answer. Hopefully that made perfect sense.

We know we've been told that you is wants to acts, which means d'you is negative to Jax and D axe is negative 1/2 to you. Which means we can pull the constant negative 1/2 on the outside of the general and the multiple body and a girl of you to the ninth D'You used the power rule. Increase the exponents by one divide by the new exponents substitute and for you.


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