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49 dx The value of the integral 2 is 2OA No correct Answer 0 B. 49 / 12 0 C.-49 / 8 0 D.-49 / 12 0 E. 49 / 8...

Question

49 dx The value of the integral 2 is 2OA No correct Answer 0 B. 49 / 12 0 C.-49 / 8 0 D.-49 / 12 0 E. 49 / 8

49 dx The value of the integral 2 is 2 OA No correct Answer 0 B. 49 / 12 0 C.-49 / 8 0 D.-49 / 12 0 E. 49 / 8



Answers

$7-48$ Evaluate the indefinite integral.
$$\int \frac{d x}{a x+b} \quad(a \neq 0)$$

But given in different we make this after person used for 21 My next week's for different getting bored cells will have. Do you goto minus two the X. So do you buy minus? Do you to go to the X that even integral becomes minus one by two? And there's enough you What about nine? Do you tell the court of minus one by two and look at the product in my 10? Let's see. Yeah. Four to minus one by 21 minus two X to the power. Let's see you don't find an answer.

Okay, so for this integral A and B are these are both going to be constant. So we're taking the derivative with respect to X. Um here where A. And B are constants. And so what we're gonna do is we're gonna use a U. D. U. Substitution with U. Equaling A X plus B. Then D. You hear is equal to A. And we can even say eight times DX. So then dx is equal to D. You divided by A. And so we're gonna make this substitution and we're now going to have the integral of one divided by you and then multiplied by D. You divided by A. And again A. As a constant here. So I'm gonna take this one divided by a constant out of this integral. And now we're just looking at the integral of D. U divided by U. And the integral of D. U divided by you or of one divided by U. Times D. U. Is equal to the natural log of you. And the reason for that is because the derivative of the natural log of U. Is equal to one divided by you there, um Kind of anti or opposites into girls and derivatives. And so we also have plus C. Here and now. We can go ahead and plug in what U. Is equal to. So this is equal to one divided by A. Times the natural log of X plus B and then plus C.

All the given individual be melted substitution you, which is all to three x plus. Be excused The French setting both sides. You have deal each 4 to 3. That's three b expert DX. Now do you remember lieutenants taking three a month? The plus the expert, the X So do you buy? Treat Is the culture a plus b X squared bx So using this after person Here you get one by three Integration of BU by duty Jakarta one by three toe to let's see so that you live for 2 to 5323 X must be excused with the power one way to let's see no for an answer.

We want to integrate this function. But notice that the you know, the rise into X Thanks, minus views. So you can see that the explain concern. So we're just actually integrating in what, x minus B, and that would just be a long model X minus B plus C.


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