5

343/472dx 9+16x2 -3/4...

Question

343/472dx 9+16x2 -3/4

343/4 72 dx 9+16x2 -3/4



Answers

$7-38$

$$
\int \frac{x-9}{(x+5)(x-2)} d x
$$

We want to integrate this function first. We can simplify. Bye. Taking this up with this. So what we'll get is this. Look at one minus four over. Denominator can be effective. Rise into X. Where X minus two. Yes. So what? We are really integrating. Is this so? But for this time, we cannot integrate directly. So let's use partial affection. It's gonna let please come here equals toe a over X does be over. X crevasses a repeat. The route Percy over explains to cross at least to the right. You will get four is equals. Toe this. Thank you. Now we're gonna let Yeah, X equals zero. Well, let s go. Zero this term. And this time goes to zero. So we have four is equals to be comes minus two. So be is minus two. Next time, don't let it supposed to do this. Time will go to zero destroyed. Go to zero. I had four is It goes to see terms to square. So my sees one. Next, A little text. It goes toe one. So I'm just gonna suck in one. So I have phone is equals to a one minus to plus B one man is to pass C, but my b is money to and my sis one. So my a it's minus one. So now I'm ready to integrate. 34 one minus. So I'm have this A is minus one of the X. This man is true. Or were X square. She is one over X minus two e x. Let me just move in the minus sign so it's easier to integrate. I'm gonna express one of the express A departments to So is easier to integrate. Okay, now I'm ready to integrate, so I would have X plus belong more X plus two extra Paul minus one over minus one. Minus long. Model X minus two. And I'm gonna put in my a pulling me a phone locally, Me off three. Now, once you put that in, you realize that, um, you will get something like Dublin over six plus long toe minus 13 And so you can group the lawn into to over three

We want to integrate this function, but we can't do it directly. So express the function as a partial fraction first. So let's high school pass one over X mas tree. It's minus two squared equals Do a over X ministry Must be over X minus to plus C over X minus two squared Because as ministers repeated route now you're just gonna cross the denominator to the right side. You will get this. Yes. Yes. Next. I'm gonna let my ex b three so that this term and this time goes to zero. Next sight serving entry on the 10. Just to eight. So my 18 next I didn't let my XP two on the lesson five on the right side this time. And this time goes to zero, leaving me with only minus c. So C is minus five. Next, let x zero. So I'm going to stop zero into every X I see in here. I'll get one in close to four e plus 60 B minus tree. See, now I already have my AMC. So stopping in and simplifying that leaves me with the is minus nine. So now I can integrate East 10. These minus nine. Now my C is minus five. The wonderful Ex managed to square. I'm just going to write the X managed to department to so it's easier toe integrate. So now the first time when integrate, I'll get this second time when I integrate, I'll get this. The time when I integrate, I'll get this. So just simplifying experience to power is just wonderful experience to plus C. So this is our final answer.

We want to integrate this function recognizes the improper function. So let's perform long division. Exhale. Yeah, Put a minus sign. We get minus four eggs less full. So really, we can rewrite this as thanks. Minus four X over X squared plus four plus full. Over. Explain this for I want to use some forms for this one. I want to try and fit into this form so I can't use the one motor ethics for this one. I want to try to feed into this bomb. Yeah, it was one of the a dungeon. Impressed. That's over. A thistle is the Yeah, so you can see that if I let FX be, I squared. Plus for my entrance B two x so I can write this fall. Yes, I can split it into so explain putting Children. Yeah, and for this peaceful Okay, we write it as two square. So I can 50 and do this one here where my is three. So now that I have this form, I can write my answer ass integrating ex. I'll get it's square over to integrating this portion. I'll have minus two fitting the form will be long mark off X squared plus sport now, but I want to highlight the X squared plus four will always be positive, so we do not need to write more. We can write it as a second, and for this term it will be plus for 15. With this one, it will be one over to tension in verse X over to So our final answer is X squared over two man is too long X squared plus foreign break it plus two tension in verse X over to Don't forget to put your plus c

Yeah, we want to integrate this function, But first, let's pick it into this partial fraction. So I'm gonna let the function. But is that the denominator can be at the rise into X squared plus one a squared plus two. So go let it be in X plus B over X squared last one plus C x plus D over X squared plus two. So crossing up the denominator to the right side, you will get this key now because there are four unknown. So there will be four equations that you need to do. You can let x be anything. So let zero sup into the into the equation. Here you will get four equals toe be. Plus de is the person equation. When you let Mexico's toe one stop in and rearrange, you will get this. So that's the second question you look XB minus one. You will get this that is that the equation? And when you let it be to you will get this. Yeah, So there's 1/4 equation. Put that into a calculator that can solve these. You get these one this one SES minus one, these two. So now we're ready to speak on function into its special collections, and that will be one plus X over X squared plus one plus minus X plus two over X squared plus two. So for the first time here, I'm going to split it into X over X squared plus one and then this one B plus one over X squared plus one. For this 10 year, it will be minus X over X squared plus two and I will have yes, two over X squared, plus two for the first time, que we want toe 50 into the form off. That's fine over events. And when you can fit the in, you can use the result long model of ethics. So the F time is X squared plus one. So the f is f X squared plus one. That time will be two weeks. So I need to have a two here. But we're happy. So the first thing is done for the second term is pretty easy is tend universe X for the top time. Again, if I want to have a time over Brexit this one here, I need a two year. So I would have here for the last time My two can be written as square to square. So it will fit the form off one over X square, plus a square where we integrate that it would be one over a engine in this picks. Overly. So now we're ready to integrate for the first. Um, Well, do you have? It is hot off the crime over FX. So that will be come on off square last night. Not normally will put more here, but because X squared plus one is possible, so we just okay, Plus, for the second tone, it just be danger investments for the victim here. This part here it's the time over. Iraq's also so it will be minus. Huh? Long off. X squared plus two best. And for the master plus two. So one of the X squared Plus with two square this fits system, so will be 1/8 is chosen. You too. I'm doing this X over to Yes, we know two over route to is just with two. So I can change this story too. And so this is all gonna answer


Similar Solved Questions

5 answers
What is the value of K for this aqueous reaction at 298 K?A+BC+DAGe =29.99 kJ /molNumber
What is the value of K for this aqueous reaction at 298 K? A+B C+D AGe =29.99 kJ /mol Number...
5 answers
2+ Co(HzO) 6] l(aq) 4Cl(aq) [CoCIa Kaq) 6HzO() (red (blue=
2+ Co(HzO) 6] l(aq) 4Cl(aq) [CoCIa Kaq) 6HzO() (red (blue=...
5 answers
OahnNolotaIdOo ebtst#ouamaV
oahn Nolota IdOo ebtst #ouama V...
1 answers
Find $d y / d x$. $$y=\ln x^{2}$$
Find $d y / d x$. $$y=\ln x^{2}$$...
5 answers
What is a lunar calendar? What is the Metonic cycle? Explain why the dates of Ramadan cycle through our solar calendar while the dates of Jewish holidays and Easter remain within about a month period.
What is a lunar calendar? What is the Metonic cycle? Explain why the dates of Ramadan cycle through our solar calendar while the dates of Jewish holidays and Easter remain within about a month period....
5 answers
HBpdra}DETAILSMcktric8 1,1.038 Erchonaueden Uha tro-pertor twnt IranAaniatJidnelneleuheairentertolirItothe
HBpdra} DETAILS Mcktric8 1,1.038 Erchonaueden Uha tro-pertor twnt Iran Aaniat Jidnelneleuheai rentertolir Itothe...
3 answers
Find matrix such that PTAP orthogonally diagonalizes A_ Verify that PTAP gives the proper diagonal form_ (Enter each matrix in the form [[row 1], [row 2],_1 where each row is comma- separated list. )(P, PTAP)[[-+J[+ ] [Co01[o 21] | Need Help? Read It Watch It
Find matrix such that PTAP orthogonally diagonalizes A_ Verify that PTAP gives the proper diagonal form_ (Enter each matrix in the form [[row 1], [row 2],_1 where each row is comma- separated list. ) (P, PTAP) [[-+J[+ ] [Co01[o 21] | Need Help? Read It Watch It...
5 answers
Name the missing coordinates if $ riangle D E F$ is isosceles with vertex angle $E$.
Name the missing coordinates if $\triangle D E F$ is isosceles with vertex angle $E$....
5 answers
Find the third degree Taylor polynomial T3(v,y,2) for thefunctionu(z,y,2) = x2y222 f(o,-1,1).at the point v
Find the third degree Taylor polynomial T3(v,y,2) for the function u(z,y,2) = x2y222 f(o,-1,1). at the point v...
5 answers
Caala Me pH 4 2 5 Rneany mnaJ008030" [email protected] TK #HC10629* 10801 60
Caala Me pH 4 2 5 Rnean y mnaJ00 8030" HCO [email protected] TK #HC10629* 10 801 60...
5 answers
Did Induensiou- SimnilarlyMATsi € d(7.14)produces rutanal ahut the #ris U angle together with rellecticn through thc (T.W) plane; #Gniu finc] tle rotation auglo A= duenslns
did In duensiou- Simnilarly MAT si € d (7.14) produces rutanal ahut the #ris U angle together with rellecticn through thc (T.W) plane; #Gniu finc] tle rotation auglo A= duenslns...
5 answers
An electron in the ground state of hydrogen has speed of 1860 km_In the excited state with n =what is the speed of an lectron?266 km/s38.0 km/s1.30x104 km/s9.11x104 km/s
An electron in the ground state of hydrogen has speed of 1860 km_ In the excited state with n = what is the speed of an lectron? 266 km/s 38.0 km/s 1.30x104 km/s 9.11x104 km/s...
4 answers
04 The scores on university entrance exam are normally distributed with a mean of 72 and a standard deviation of 15 Find the probability that a student taking the entrance exam will score below 81_ Find the probability that a student taking the entrance exam will score between 65 and 71_ Find the grade of a student such that the corresponding probability is higher than 69%_
04 The scores on university entrance exam are normally distributed with a mean of 72 and a standard deviation of 15 Find the probability that a student taking the entrance exam will score below 81_ Find the probability that a student taking the entrance exam will score between 65 and 71_ Find the gr...
5 answers
%) Problem 30: Considcr proton with momentum of 4.48 x 10-19 kg mls_What is thc spccd in metcrs per sccond, of this proton?Grade Summary Deductions Potenlial IUU %sino coso) tanO) cotano asino) acoso atano) acotan() sinho) cosho) tanho cotanho Degrecs RadiansHOMESubinissions Atlempts remaining: 5 per a.empl) A iled viewENDBACKSPACECLEARSubrnitHintFeedback1give up'Hints: U50 deduction per hin: Hinls rerainingFeedback: 4Z_ deduction per feedback:
%) Problem 30: Considcr proton with momentum of 4.48 x 10-19 kg mls_ What is thc spccd in metcrs per sccond, of this proton? Grade Summary Deductions Potenlial IUU % sino coso) tanO) cotano asino) acoso atano) acotan() sinho) cosho) tanho cotanho Degrecs Radians HOME Subinissions Atlempts remaining:...

-- 0.020604--