A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
how to do this integral?
anonymous
 one year ago
how to do this integral?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}\frac{ x^2 + 1 }{ (x3)(x2)^2}dx\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.4how are you at partial fractions?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i understand it a bit (split into parts, right? A/B?) but don't know quite how to apply it!

misty1212
 one year ago
Best ResponseYou've already chosen the best response.4it is going to suck want to do it step by step, or cheat?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you show me how to do it step by step?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.4\[\frac{A}{x3}+\frac{B}{x2}+\frac{C}{(x2)^2}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.4that means \[A(x2)^2+B(x3)(x2)+C(x3)=x^2+1\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.4let me know if that is clear, then we can continue

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is clear:) what happens next?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.4we can get C right away by putting \(x=2\) because the A and B will drop out

misty1212
 one year ago
Best ResponseYou've already chosen the best response.4if you put \(x=2\) you get \[C(23)=2^2+1\] or \[C=5\] making \(C=5\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes:) sorry, OS connection was very poor!! what happens next?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1get A by setting x = 3 same technique

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so then i get 3^2 + 1 = 10 ?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\[A(32)^2+B(33)(32)+C(33)=3^2+1\] \[\checkmark\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok!! what do i do next?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\[10(x2)^2+B(x3)(x2)5(x3)=x^2+1\] you need B so set x to anything really. but let's just go with x = 0.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1sure? 10(4) + B(3)(2)  5(3) = 1 6B = (1 15 40)????

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh oops!! it equals 55!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@IrishBoy123 i have to leave for an appointment now, but will be back in a few hours!! is it okay if we continue then, or if i come back and see what you say?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\[\color{red}6B = 5 \color{red}4\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@IrishBoy123 I'm back!! can you please help me explain the rest?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so B = 9 right? what happens next?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1let's agree where we got to first

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{10}{x3}\frac{9}{x2}\frac{5}{(x2)^2}\] are we sure that's a good summary?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay! so A=10, B=9 and C=5 ?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1now you must do \[\int \frac{10}{x3}dx \int \frac{9}{x2}dx\int\frac{5}{(x2)^2} dx\] 3 separate integrals

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ooh okay, how do i start off?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1first one \[\int \frac{10}{x3}dx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so we get 10lnx3 ?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\[\int \frac{9}{x2}dx\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1first part is right, do the second now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh i see now and so now second we get 9lnx2 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and for the third, we get 5/(x2) ?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1yes. just make a note that we need to put the correct signs between the integrals righ at the end as it is ∫dx  ∫dx  ∫dx last one \[\int\frac{5}{(x2)^2} dx\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1yes put it all together now

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1don't bother writing it out if you are happy with it all

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}10lnx3 dx  \int\limits_{}9lnx2dx + \int\limits_{} \frac{ 5 }{ x2 }dx\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1no, drop all the integration signs now that you have integrated so \[10 \ln(x3)  9\ln(x2) + \frac{ 5 }{ x2 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okay!! what now? :)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1i think the fat lady is now singing.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hahaha ohh so we are done?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1OMG!!!! we forgot something....

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1the integration constant!!

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1how embarassing after all that :))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okie!! yay!! thank you so much!!

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1you and misty did all the heavy lifting, we just finished it off:) good night!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.