A community for students.
Here's the question you clicked on:
 0 viewing
mrtuba
 2 years ago
integral of (3x^3+2x^2+7x+13)/((x1)^2(x^2+4)^2)
mrtuba
 2 years ago
integral of (3x^3+2x^2+7x+13)/((x1)^2(x^2+4)^2)

This Question is Closed

candrie
 2 years ago
Best ResponseYou've already chosen the best response.0http://myalgebra.com/algebra_solver.aspx Plug your problem in here

mrtuba
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{}(3x^3+2x^2+7x+13)/((x1)^2(x^2+4)^2)\]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Did you try partial fractions Are is partial fractions what you need help on?

mrtuba
 2 years ago
Best ResponseYou've already chosen the best response.1i did partial fractions but its so incredibly terrible that the expanded for after cross multiplication took up to line of college rule paper written in small print. I feel like there is some simplifying i could do before doing partial fractions

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3It does look like it can nasty but I don't see any other way to go about it but... just because i don't see any other way doesn't mean it doesn't exist

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3\[\frac{3x^3+2x^2+7x+13}{(x1)^2(x^2+4)^2}\] \[=\frac{A}{x1}+\frac{B}{(x1)^2}+\frac{Cx+D}{x^2+4}+\frac{Ex+F}{(x^2+4)^2}\] Yeah this is going to be ugly

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3So you didn't find those constant values for A,B,C,D,E and F right?

mrtuba
 2 years ago
Best ResponseYou've already chosen the best response.1no i just saw the set up after cross multiplying and expanding looked so crazy that i thought i had to have missed something that could make it easier.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3\[=\frac{A(x1)(x^2+4)^2}{(x1)^2(x^2+4)^2}+\frac{B(x^2+4)^2}{(x1)^2(x^2+4)^2}+\frac{(Cx+D)(x1)^2(x^2+4)}{(x1)^2(x^2+4)^2}+\frac{(Ex+F)(x1)^2}{(x^2+4)^2(x1)^2}\] \[3x^3+2x^2+7x+13=A(x1)(x^2+4)^2+B(x^2+4)^2+ \] \[(Cx+D)(x1)^2(x^2+4)+(Ex+F)(x1)^2 \] And then continue from here ....

mrtuba
 2 years ago
Best ResponseYou've already chosen the best response.1yeah i went past that, just looks like this one will be ugly i guess ill just keep chugging thanks.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Sorry... I'm not able to offer an easier way :(

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3I don't think there is one...

malevolence19
 2 years ago
Best ResponseYou've already chosen the best response.0Plug in X=1 to get a value, x=0 might also help

mrtuba
 2 years ago
Best ResponseYou've already chosen the best response.1can not figure out the system of equations this leads me to

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.21. Carefully check your + and  signs in the original problem. You've currently an unfactorable polynomial in the numerator with a larger, higher degree polynomial in the denominator. I'd agree with @myininaya's approach. One missed sign could make it factorisable such that something could simplify/cancel out and the whole thing become much more feasible. 2. There isn't an easier way, that I can see either, you're just going to have to solve that system of equations, namely you're going to have to use both methods of combining systems of equations and making substitutions, AND using known vertical asymptote values for the denominator (in this case +1 and 2i). Yes, I'm serious, use an imaginary root here, you kind of have to. Post your system of equation here, and try those roots, see what happens (things cancel out). 3. Using that I got: A = 0 B = 1 C = 0 D = 1 E = 1 F = 1 You'll also need to make use of this fact: \[\frac{d}{dx}(\frac{1}{a} \tan^{1}(\frac{x}{a})) = \frac{1}{x^2+a^2}\] This problem as written is doable, but it's a lot of work and will also most likely also force you to remember some antiderivatives which have trig function forms and make use of halfangle and doubleangle formulas too. So you got a lot of work to do, better get to it eh? ;D

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0Here is a summary and a conclusion to what have been above and what have not been \[ \frac{3 x^3+2 x^2+7 x+13}{(x1)^2 \left(x^2+4\right)^2}=\frac {x+1}{\left(x^2+4\right)^2} \frac{1}{x^2+4}+\frac{1}{( x1)^2}\\ \int \left(\frac{x+1}{\left(x^2+4\right)^2}\frac{1}{x^2+4}+\frac{1}{(x1)^2}\right) \, dx=\\\frac{x4}{8 \left(x^2+4\right)}\frac{1}{x1}\frac{7 }{16} \tan ^{1}\left(\frac{x}{2}\right)+ C \]

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.2@eliassaab is 100% correct :)
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.