Partial fractions Definition and 298 Threads

Homework Statement In one of the workings of a question I couldn't solve(from solution sheet) there was one step I couldn't understand. Homework Equations \frac{1}{x^2+x+1} = \frac{1-x}{1-x^3} The Attempt at a Solution Tried partial fractions(unfactorable denominator) and could'nt get it...

Homework Statement ∫(x3+4)/(x2+4)dx Homework Equations n/a The Attempt at a Solution I know I have to do long division before I can break this one up into partial fractions. So I x3+4 by x2+4 and got x with a remainder of -4x+4 to be written as x+(4-4x/x2+4). Then I rewrote...

Homework Statement We were given a worksheet to integrate some problems using partial fractions. This one however I cannot figure out what to do with it. This is the problem. ∫(x3-4x2+x+6)/(x2-x+2) dx The Attempt at a Solution using long division i got ∫(x-3) (-4(x-3)/(x2-x+2) dx...

$$ \frac{1}{z^2(1-z)} = \frac{A}{z^2}+\frac{B}{1-z} $$I can't figure out how to decompose this fraction.

Homework Statement If f is a quadratic function such that f(0) = 1 and \int \frac{f(x)}{x^2(x+1)^3}dx is a rational function, find the value of f '(0). Homework Equations The Attempt at a Solution This question is presented in the context of learning about integration by...

Homework Statement Evaluate the integral. (Remember to use ln |u| where appropriate.) ∫(x^3 + 36)/(x^2 + 36) Homework Equations The Attempt at a Solution A little bit confused about arriving at the solution for this problem. I get stuck a little ways in. Any help would be...

y' = (3+y)(1-y) y(0) = 2 Attempt to solve: \frac{dy}{dx}=(3+y)(1-y) (3+y)(1-y)dy = dx \int(3+y)(1-y)dy = \int dx Partial Fractions: \frac{A}{(3+y)} + \frac{B}{(1-y)} A(1-y)+B(3+y) Let y= 1 or -3 A = 1/4 B = 1/4 \frac{1}{4}\int \frac{1}{(3+y)} dy + \frac{1}{4}\int...

Homework Statement \frac{x}{(x+4)^{2}} Homework Equations The Attempt at a Solution I make the integrand equal to the following: \frac{A}{(x+4)}+\frac{Bx+C}{(x+4)^{2}} Then after finding a common denominator I get x = A(x+4)^{2}+(Bx+C)(x+4) But that cannot be...

Homework Statement So I am trying to integrate the following. I believe I have to use partial fractions. \frac{1}{(x+4)^{2}(x-3)} Homework Equations The Attempt at a Solution So I am trying to expand the above into something that I can integrate. So I equated the integrand...

I just want to know if there is now a way to solve fractions like which had a variables that has a degree more than 2 in its denominator. I know that denominators having degrees of 2 could be solved using (Ax + B)/(x2+a). But how about denominators like (x3+a) and so on?

Hello all, Say one wants to find the inverse Laplace Transform of a function, and the method for attaining the solution is executed via partial fractions. Do the real numbers go with the complex numbers when determining the constants of partials? Perhaps this is wordy. I'll provide a theoretical...

Homework Statement Use partial fractions to rewrite: (2z)/(z^2+3) Homework Equations noneThe Attempt at a Solution I did this: (2z)/(z^2+3) = (Az+B)/(z^2+3) 2z = Az +B A = 2, B = 0...problem is that it just recreates the original Here is their example in the book: 1/(z^2+1) =...

Homework Statement Find partial fractions for 4/(x^3-2x^2) The Attempt at a Solution Heres the steps that I took: 1. 4/(x^3-2x^2)= 4/(x^2(x-2))= A/(x^2) + B/(x-2) 2. 4= A(x-2) + B(x^2) 3. When x=0, -2A=4, so A=-2, and When x=2, 4B=4, so B=1. 4. So my final answer was: -2/(x^2)+1/(x-2) The...

Hey everyone, I was wondering if someone could help me understand what exactly is happening with a certain integral I am working with, which is as follows: ∫2/(u^2-1)du My steps are as follows (I used partial fractions): ∫(1/(u-1) - 1/(u+1))du = ∫1/(u-1)du - ∫1/(u+1) = ln[(u-1)/(u+1)]...

Homework Statement the definite integral of (x-1)/(x^3+4x^2+3x) from x=1 to x=3 using partial fraction decomposition. I know the answer should be (5/3)ln2 - ln3. Homework Equations The Attempt at a Solution After integrating, I got -(1/3)ln(3x) - (2/3)ln(x+3) + ln(x+1) . The...

Hi, I have a question regarding partial fractions. One of my Math lecturers said that to find partial fraction, we are actually finding the singularity points. I don't understand what happens at a singularity point that allows us to decompose a function into the sum of two other functions...

Homework Statement Expand Using Partial Fractions: f(x) = ( 5x-10 )/ ( (x+1)(x-4) ) Involves Integrating afterwards but I don't think this affects my method.Homework Equations This was a question in my mid semester exam, I got the answer correct but he insists my method is wrong.The Attempt at...

Homework Statement Integrate (x^3 - 8x^2 - 1)/((x+3)(x^2-4x+5)) Homework Equations This is an integration by partial fractions. The Attempt at a Solution http://www.wolframalpha.com/input/?i=integral+%28%28x^3-8x^2-1%29%2F%28%28x%2B3%29%28x^2-4x%2B5%29%29%29dx I understand everything...

\frac{-2x^2-x-3}{x^3+2x^2-x-2}=\frac{-2x^2-x-3}{(x-1)(x+1)(x+2)}=\frac{A}{x-1}+\frac{B}{x+1}+\frac{C}{x+2} Multiply by common denominator gives: -2x^2-x-3=A(x+1)(x+2)+B(x-1)(x+2)+C(x-1)(x+1)\Leftrightarrow -2x^2-x-3=Ax^2+A3x+A2+Bx^2+Bx-B2+Cx^2-C1 System of equations gives -2=A+B+C -1=A+B...

Homework Statement Find the partial fractions of 1/((3x)(5-x)) Homework Equations The Attempt at a Solution 1/((3x)(5-x))=A/(3x)+B/(5-x)=(A(5-x)+B(3x))/((3x)(5-x)) 1=A(5-x)+B(3x) If x=0 1=A(5-0)+B(3*0)=5A => A=1/5 If x=5 1=A(5-5)+B(3*5)=B15 => B=1/15 So...

\int\frac{7x^2+4x+5}{x^3+x} dx I have to solve this using partial fractions and all I could think of was breaking it up into: \frac{A}{x}+\frac{B}{x^2+1} also I tried \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x} The reasoning behind this one was to split up original...

Homework Statement \int\frac{4x^5-1}{(x^5+x+1)^2}dx Homework Equations This is in the section on Partial Fractions. The main idea in this section was that you get the integral down to a sum integrals of the following forms: \int\frac{dx}{(x+a)^n} , \int \frac{x dx}{(x^2 + bx + c)^m} ...

Homework Statement Evaluate integral dx/(x^4-10x^2+9) Homework Equations The Attempt at a Solution Ok so I'm trying to solve this problem for my calculus II course as a homework problem and am lost. The first attachment you'll see how I attempted to evaluate the integral by...

Homework Statement seperate and solve using partial fractions dx/dt=9-4x2, x(0)=0 The Attempt at a Solution rearranging gives dx/(9-4x2) = dt factorising denominator in preperation for partial fractions becomes dx/(3-2x)(3+2x) then A/(3-2x) + B/(3+2x) dx so A(3+2x)+ B(3-2x)...

Homework Statement Someone teach me how to write equations using the editor here... This is part of an integration question need partial fractions of 1/(x^2)(x-4) Homework Equations -nil- The Attempt at a Solution 1/(x^2)(x-4)=(Ax+B)/(x^2)+C(x-4) Put x=0 therefore B=-1/4...

Integrate using partial fractions (arctan x) / ((x+1)(x^2+1))? My attempt: (arctan x) / ((x+1)(x^2+1)) = A/(x+1) + (Bx+C)/(x^2+1) arctan x = A(x^2+1) + (Bx+C)(x+1) when x= -1, A= -pi/8 so plugging in -pi/8 for B makes: x= tan[ (B-(pi/8))x^2 + (B+C)x + (C-(pi/8)) ] and when x=0, C=...

Hi, this is my first post, and I'm not sure if I'm posting this in the right place. Homework Statement I have a 2nd order diff. equation: 3y''(t) + 2y'(t) + 5y(t) = 3 with initial values: y'(0) = 1, y(0) = 0 Homework Equations After using Laplace transform I get: Y(s) = (3 +...

I have a few questions about decomposing partial fractions. I know how to solve these problems, but I just don't understand why I'm doing some of the things. 1. Why does equating coefficients work? I don't understand the idea behind it. 2. When you are decomposing fractions into constants...

Homework Statement find the laurent series of sin(2z)/(z^3) in [z]>0 Homework Equations The Attempt at a Solution I am completely confused. I can understand some of the examples given on laurent series, like using partial fractions and then finding geometric series. Do I rewrite...

Homework Statement evaluate: \int \frac{x^3}{x-1} dx this is part of a bigger question... i get down to this far but i have no idea how to tackle this integral...Homework Equations The Attempt at a Solution my thoughts are - partial fractions... but its only got one thing on the...

Homework Statement ∫ 5e^2x / (25e^2x - 20e^x +4) dx Homework Equations The Attempt at a Solution The attempt at the the solution is in the attachment below. I am stuck at that step. Pretty much can anyone tell me what 'something' should be. I know if the denominator were a...

Homework Statement Find the volume of the resulting solid if the region under the curve y=1/(x^2+3x+2) from x=0 to x=1 is rotated about the x-axis. R=(1/(x^2+3x+2) Equation for volume using the slicing method... 3.14 INT((1/(x^2+3X+2))^2)dx over the interval 0-1 Homework Equations...

Homework Statement Hello I'm trying to figure out how to integrate with the use of partial fractions but I'm a bit stuck on something that should probably be simple.. but I can't see it clearly How do you split up x2-8/x+3 and make it equal to (x-3) + 1/x+3 or for instance x2 +1/x-1 split up...

Homework Statement \frac{gx^2+1}{x^3(x-1)^2} I'm trying to keep g as a coefficient, it's turning into a mess though. The Attempt at a Solution After I broke it down it gives: Ax^2(x-1)^2 + Bx(x-1)^2 + C(x-1)^2 + Dx^3(x-1) + Ex^3 = gx^2 + 1 After using x =1, everything goes away and I'm...

1. find the inverse FT of 1/(iw+3)3 2. well partial fractions gave the same thing back... I'm not sure how to transform this as there's no property that deals with cubics. 3. i tried using the differentiation property but it doesn't work as it increases the power of 3 to 4 and so...

Homework Statement (〖5x^3〗+〖4x^2〗-4)/((x^3)(x+1)) Homework Equations Partial Fractions The Attempt at a Solution I know that I need to use partial fractions. But I don't know how to put it in (A/x)+(B/x)...etc Would someone please kindly show me how to set up this equation...

Homework Statement Solve this IVP: y'=(y-9x)^2 ; y(0)=1 Given a hint: Use the substitution v=y-9x and partial fractions. Homework Equations ... The Attempt at a Solution I was able to solve this DE through partial fractions, etc until I ended up at this point ln (v-3/v+3)...

I am trying to use partial fractions to expand (3200x+16)/(x+400)^2 on the ti-89 calculator but I keep getting .010075 as the answer when I use the expand function! What am I doing wrong here?

Trying to help out a friend. I appolagise if yet again this is in the wrong part of the forum, i haven't an idea what it is categorised as, I am an apprentice engineer and simply that lol Can someone explain how the following is done: x^2 – x + 1 / (x - 2)(x^2 + 1) ≅ A / (x - 2) + Bx +...

Homework Statement write out the form of the partial fraction decomposition of the function, do not determine the numerical values of the coefficients x^2/(x^2 + x + 2) Homework Equations The Attempt at a Solution since the numerator is not less of a degree than the...

So I am being asked to use partial fractions to solve ODE's. In particular, I have (dx/dt) = 3x(x-5) with x(0) = 2. I came up with A = -1/5 and B = 15. Then, I had (1/15)*[(x-5)/(3x)] = Be^t. But this is where things break down. I thought B = -1/2. Yet the book's answer is...

Integration of Rational Functions by Partial Fractions? Ok I'm working on some homework problems and I don't even know how to do the first one, here is my problems and the steps that I did thus far ( I don't know if I did them right) 5x-13/(x-3)(x-2)= A/x-3 + B/x-2\rightarrow ...5x-13=...

Homework Statement I'm just curious if there is any useful shortcuts when applying partial fractions decomposition. These are only a portion of the problem given for us, so it's important that I can do them quickly and efficiently. Does anyone know of any useful shortcuts that would speed...

Q: Find the Integral of (26x+36)/[(3x-2)(x^2+4)] dx Here is my attempt: First i set it up so that, (26x+36) / [(3x-2)(x^2+4)] = A/(3x-2) + (Bx+C)/(x^2+4) Then, 26x + 36 = A(x^2+4) + (Bx+C)(3x-2) = Ax^2 + 4A + Bx^2+Bx+Cx+C <---(This is where I...

Homework Statement I am stuck on this integral. 1) (a - bx)/(a^2 + b^2 - 2abx)^(3/2) I tried some substitutions but end up with complicated expressions. How to decompose into partial fractions when the denominator is raised to fractional powers? Can anyone please help me out? Homework...

Homework Statement \int_0^1 \! \frac{x-4}{x^2+3x+2} dx Homework Equations The Attempt at a Solution Factoring out the denominator... x^2+3x+2 = (x+1)(x+2) Breaking up the main fraction into the separate fractions. Since both are linear, only a single constant is...

Homework Statement \int(5x+2)/(x^{2}+25)^{2}dx Homework Equations The Attempt at a Solution \int5x/(x^{2}+25)^{2}dx+2\int1/(x^{2}+25)^{2}dx I can integrate the first part using u substitution then I am stuck at the second part...my partial fraction answer is the same as the...

Homework Statement Ey guys I am trying to derive a potential flow equation and in the process i need to integrate with respect to 'x'. I need to integrate what is shown below with respect to x Homework Equations -\frac{y^2}{(x^{2} + y^{2})^{2}} The Attempt at a Solution...

I'm having issue with one problem. We're asked to break down the problem into partial fractions to solve for the integral. Well, I'm stuck on one. I'm being asked for the values of A, B, and C for the following problem. ∫((9x^2+13x-83)/((x-3)(x^2 + 16)))dx I can get it worked down...

Homework Statement find the integral of (1 + 2x)/(1+x^2) Homework Equations The Attempt at a Solution I honestly have no idea how to solve this and have spent ages trying to figure it out. I would automatically assume using partial fractions to solve but the denominator presents...