5

X? (3x' + 9)5 dr =Select one: a. None of these ('+L+C (3r'+9)6 +C (3x'+9)0 +C...

Question

X? (3x' + 9)5 dr =Select one: a. None of these ('+L+C (3r'+9)6 +C (3x'+9)0 +C

x? (3x' + 9)5 dr = Select one: a. None of these ('+L+C (3r'+9)6 +C (3x'+9)0 +C



Answers

Write the integral $\int \frac{2 x+9}{(3 x+5)(4-5 x)} d x$ in the form $\int \frac{c x+d}{(x-a)(x-b)} d x .$ Give the values of the constants $a, b, c, d .$ You need not evaluate the integral.

Uh When you're asked to find the integral of X plus one squared dx Using U substitution I would just let U equal X plus one. So then do you would just be dx a derivative of both sides are equal. So when you go to find the integral it's still going to be squared but the U. Value instead of X plus one you can rewrite as you and then dx is just equal to D. You. So then the integral that you add one to the exponents and divide by your new exponent plus C. Which if you go back um you need to go back and replace your you with X plus one cubed plus C. So that's your answer to part A and part B. What they wanted you to do is actually you distribute it out would be X squared plus two. X plus one. Remember this is X plus one times X plus one. I'm assuming you can do that in your in your head because if you do the integral of that um you would add one to the exponents divide by your new exponents, Add 1 to the exponent divide by your new exponents, Add 1 to the exponents. Well it's just X. And then plus C. And I know this doesn't quite look the same, but they are equivalent because if I went through and asked you and you probably use pascal's triangle or something like that, where you would rewrite as three X squared plus three X plus one. uh well the constants are different because as you distribute this 1/3 in here You get 1 3rd plus a constant which is just a different constant, but they are equal in essence um You know because of that arithmetic I guess would be the best way to explain it.

We have Hi So I It's equal today in Segre X. My next nine divided by X plus five. You have X -2 the X. So we can write a partial fraction for this solis right pasha fraction for X. My next nine divided by X plus five. You have AIDS -2. This is going to be E divided by X-plus five Plus B divided by X -2. So this is our past a fraction. Sophos Yeah, a pasha a partial fracture. So then you can find the values of mm and be from here. So to do that, you are saying X -9 should be equal to Hey you have X -2 plus d. You have X plus five. So when you solve for the values of a. B, It implies that B is going to be called -1. Then a is going to be equal to two Sudan. This implies that our X -9. You fight it by X plus five. X -2 is going to be Sue. Mm hmm divided by X plus five. My next one divided by X -2. So they this implies that fancy a gra nine X. My next night divided by eggs last five x minus two. The X. Is going to be it's going to be the girl Sue divided by X plus five. The x minus the insignia one divided by X -2. The so I applied the sum rule here. So then This is going to be equal to two Plain x plus five minus Plane. You have X -2 plus a consequence. You can rewrite this. Splain. You have X plus five, last five squared minus lame x minus two plus a constant scene. And this you can equally because of that side indices. If you remember, then this is going to be lean. You have X plus five squared divided by X plus soon the past are constants C as the final answer.

Today we're going to solve a problem about 23 from the jump five. We have to find the integral value so we can substitute Let u equals X minus tree X equals u plus three. The egg sickles. Do you a quince tree so they can write integral. Thanks. Plus, if I They were led by we wrote off nine minus X minus strata Whose square the X tickles integral you plus three classify divided by square root off a square minus you square. Did you? Which physical toe? Integral. You plus eight. They were led by square root off a square minus you square Do you so the right us doing the girls? Okay, I did it. You will do it by square root off a square minus you square do you? Plus eight different by square root off a square minus you square, Do you so multiply and divide the first integral by minus two minus two by minus two You will get like minus two. You do You would like minus two square root off a square minus you square do you plus eight in the group. Do you developed by where Rudolph is square minus you square so difficult to my wrist. One by two integral a square minus you Square holder for minus one by two minus two You do you plus eight Integral. Do you developed by squared off a square minus you square. So this value comes to be like minus wrote off a square minus you square plus eight Sign English You buy a plus six That's good for two equals X ministry Leave it and they call ST you get minus quite a tough nine virus X minus tree the whole square plus eight window signing Worse X minus three by three, plus six so we can get like eight Signing was X minus three by three minus square root off 66 minus x square Plus it. That's the end off a question. Thank you.

Given a u of expose three. And given the fact that do you is detox and you minus three is acts we can first substitute to get the integral zero minus three. You want half times, do you? This gives us once we've integrated 2/5 you to the five over two minus three temps. 2/3 you the three over two plus c, which is equivalent to So we're substituting back ends. We're getting rid of you more. Substituting back in with the actual value is minus two times X plus three the three over two plus C Sansa trice bee.


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