Partial fractions Definition and 298 Threads

Homework Statement Homework Equations After looking through this on Wiki, I'm a little confused as to how these partial fractions are multiplied out. Is there a rule or something for this? With simpler partials I can do it but this one is something else! The Attempt at a Solution

Homework Statement f = \frac{1}{z(z-1)(z-2)} Homework Equations Partial fraction The Attempt at a Solution R1 = 0 < z < 1 R2 = 1 < z < 2 R3 = z > 2 f = \frac{1}{z(z-1)(z-2)} = \frac{1}{z} * (\frac{A}{z-1} + \frac{B}{z-2}) Where A = -1 , B = 1. f = \frac{1}{z} *...

\int (x+1/x2-3x-5)dx I can't put the limits on the integral sign, 5 is the top limit and 3 is the bottom limit. I can solve using partial fractions ok but I have never solved with limits before. Where do the limits come in, do I need them at the start or can I factorise as usual and use...

Homework Statement 1/ (x+8)(x^2+16) Find the integral Homework Equations I keep getting this question wrong. Can someone check my steps? The Attempt at a Solution I set it up as A/(x+8) + (Bx+C)/(x^2+16) So I did, A(x^2+16)+ (Bx+C)(x+8) and I did that and got A+b=0...

Homework Statement (2x^3-2x+1)/(x^2/3x) Find the integral. 2. The attempt at a solution So I've been on this problem for like an hour now and I don't know what I'm doing wrong. So I used long division and got 2x+ (4x+1)/(x^2-3x) ∫2x + ∫(4x+1)/(x^2-3x) = x^2 +...

Homework Statement I(alpha) = ∫1/((x+alpha^2)(x+1)) dx between the limits of 0 and infinity Evaluate the integral above depending on the parameter alpha using partial fractions. The Attempt at a Solution 1/((x+alpha^2)(x+1)) = A/(x+alpha^2) + B/(x+1) 1 = A(x+1) + B(x+alpha^2)...

I am trying to separate out \[ \frac{s}{(s+1)^3} \] for an inverse Laplace transform. How does one setup up partial fractions for a cubic? I know for a square I would do \[ \frac{A}{s+1} + \frac{Bs+C}{(s+1)^2} \] I tried doing \[ \frac{A+Bs}{(s+1)^2} + \frac{Cs^2+Ds+E}{(s+1)^3} \] which led to...

Homework Statement Use integration by parts to evaluate the integral ∫(7-6x) / (x2-4x+13)The Attempt at a Solution This is a question from my notes so I already have the solution but I'm not sure what's going on at this one specific step. ∫(7-6x) / (x2-4x+13) = -∫(6x-7) / (x2-4x+13) = -∫(...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Well this is part of an integration process, namely: \int \frac {sin^2x}{4+3cos^2x}dx Homework Equations My attempt involved using a u-substitution, namely t = tan x The Attempt at a Solution Using t = tan x, sin^2 x = \frac {t^2}{1+t^2} and cos^2 x = \frac...

Homework Statement ∫▒√(1+x^2 )/x dx Homework Equations The Attempt at a Solution I don't know how to break this up. I know we break partial fraction problems up based on their denominator, however the denominator i this problem is just 'x'.

Homework Statement Why when I try to evaluate this with Partial Fractions, why do I end up with the original function? \int\frac{n}{(n^{2}+1)^{2}} \frac{n}{(n^{2}+1)(n^{2}+1)} \frac{Ax+B}{n^{2}+1} + \frac{Cx+D}{(n^{2}+1)^{2}} 1n = (An+B)(n^{2}+1) + Cx + D 0n^{3}+ 0n^{2} + 1n + 0n^{0} =...

Homework Statement ∫(x+1)/(x2+2x+3)dx The Attempt at a Solution This problem was under partial fractions in my book. I solved it using u-substitution where u=x2+2x+3, but i can't see how it can be solved using partial fractions? can it?

Homework Statement ∫ 4x/(x^3+x^2+x+1) dxThe Attempt at a Solution I really don't know where to start, you can't complete the square, the degree of the numerator is less than the denominator so you can't use long division to simplify it. I can't really simplify the denominator as well, so I...

Here is the question: Here is a link to the question: Integral of ((19x^2)-x+4)/(x(1+4(x^2)))? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Write out the form of the partial fraction decomposition of not determine the numerical values of the coefficients. Homework Equations x^4 -2x^3 + x^2 +2x -1 / x^2 -2x +1 The Attempt at a Solution I did the division and I got x^2 + ((2x-1)) / (x^2 -2x +1)...

Hey guys, i have read many posts on physics forums but this would be my first post. I am quite stuck so any help would be much appreciated. Homework Statement Use Laplace transforms to solve the initial value problem: f''(y) + 4f'(y) +8y = u(t-1) where y(0) = 1 and y'(0) = -1 Solve...

Homework Statement Find the integral and determine whether Cauchy's Theorem applies. Use partial fractions. \large \oint \frac{tan \frac{z}{2}}{z^{4} -16} dz C the boundary of the square with vertices ±1, ±i cw Homework EquationsThe Attempt at a Solution I just wanted to check if approach is...

i understand the linear case... example.. #/{(x+5)(x-4)} ----> A/(x+5) + B/(x-4) but i don't understand this.. example.. #/{(x^2+3)(x^2+9)}------>(Ax+B)/{(x-√3)(x+√3)} + (Cx+D)/(x^2+9) first of all... (x-√3)(x+√3)= x^2-3, which is nowhere in the original equation.. it's...

How do I turn 1/(x4+1) into partial fractions? This is what I did. Let me know if this is correct 1/(x4+1) = 1/[(x^2+i)(x^2-i)] = (Ax+B)/(x2+i) + (Cx + D)/(x2-1) Then I set x = 0 1 = (D-B)i .. My first equation would be D-B = 0. Is that correct so far?

Determine which value best approximates the area of the region between the x-axis and the graph of ##f(x)=\frac{10}{x(x^2+1)}## over the interval [1,3]. Make your selection on the basis of a sketch of the region and not by performing any calculations. Explain your reasoning. (a) -6 (b) 6...

1) integral (upper bound:1, lower bound:0) (x^2+1)/(x^3+x^2+4x) dx 2) integral (upper bound:1, lower bound:0) (x^4+x^2+1)/(x^3+x^2+x-3) dx Now I know how to use Partial Fractions,My question is: 1) For the first part ln(x) is not defined at 0 ¼ʃ1/x dx + ¼ʃ(3x-1)/(x²+x+4) dx = ¼ ln|x| +...

Hello all, I'm working through old exams for an electrical subject (no solutions given) and I think I've gone wrong somewhere and been left with something I'd like to learn how to work with anyway: \frac{50}{(s+\frac{1}{s}+1)^2-s^2} \frac{50}{2s+3+\frac{2}{s}+\frac{1}{s^2}}\times...

Question: http://gyazo.com/bcb6c97ba462cdf4964121a6a40b0753 Mark scheme: http://gyazo.com/b0475e7cb980ce98fb443932c28deed2 What I don't understand is the question specifies that x is not equal to 1/3 or -2, so why are you allowed to sub them into get the correct value for A B and C?

Hello MHB, I got stuck on this integrate $$\int_0^{\infty}\frac{2x-4}{(x^2+1)(2x+1)}$$ and my progress $$\int_0^{\infty} \frac{2x-4}{(x^2+1)(2x+1)} = \frac{ax+b}{x^2+1}+ \frac{c}{2x+1}$$ then I get these equation that I can't solve and I get these equation.. $$2a+c=0$$ that is for $$x^2$$...

Let's start with: $$ \int \frac{dx}{1+x^2} = \arctan x + C $$ This is achieved with a basic trig substitution. However, what if one were to perform the following partial fraction decomposition: $$ \int \frac{dx}{1+x^2} = \int \frac{dx}{(x+i)(x-i)} = \int \left[ \frac{i/2}{x+i} -...

Homework Statement Use partial fractions to find the sum of the series.Homework Equations \displaystyle \sum^{∞}_{n=1} \frac{8}{n(n+3)} The Attempt at a Solution I end up with: \displaystyle \frac{8}{3n} - \frac{8}{3(n+3)} I am stuck here.

Homework Statement This is an arc length problem in three dimensions. I was given the vector r(t)=<et, 1, t> from t=0 to t=1 Homework Equations Arc Length= \int |\sqrt{r'(t)}| dt from t1 to t2 where |\sqrt{r'(t)}| is the magnitude of the derivative of the vector The Attempt at a...

1. ∫[(x4 + x + 1)/(x(x2 + 1))]dx 2. When I first did this problem, I divided and got: ∫[x + (-x2 + x + 1)/(x3 + x)]dx (x3 + x) = x(x2 + 1) I then set up the fraction as: A/x + B/(x2 + 1) BUT, the solution to this problem says: A/x + [(Bx + C)/(x2 + 1)] How would I know to use...

1. So, i have the next integrand... 2. \int \frac{1}{(x-1)^2(x+1)^2}\,dx 3. I proceeded by resolving it by partial fraction and i came up with the next... \int \frac{1}{((x-1)^2)((x+1)^2)}\,dx = \int \frac{A}{(x-1)} + \frac{B}{(x-1)^2} + \frac{C}{(x+1)} + \frac{D}{(x+1)^2}\,dx The thing is...

Homework Statement Use the method of partial fractions to show that: $$\frac{2x^2}{(1-x(1+x)} $$ , may be written as: $$-2+\frac{1}{1-x}+\frac{1}{1+x}$$ , where $$\lvert x\rvert\neq1 $$. Homework Equations The Attempt at a Solution I obviously know how to do it but in the...

I've been trying to get out this question for a while now: ai) Show that (x,y,z) = (1,1,1) is a solution to the following system of equations: x + y + z = 3 2x + 2y + 2z = 6 3x + 3y +3z = 9 aii) Hence find the general solution of the system b) Express 2x^2 + 3/(x^2 + 1)^2 in partial...

Whoa, this here is kicking me hard! Okay, so I've got everything pretty well down until... stuff like... \int \frac{3x + 32}{x^{2}-16x + 64}dx So, I get how to factor the denominator, but then what? The above won't factor... Also, I read that if the degree of the numerator is higher than the...

Homework Statement ∫ (x^3)/(x^2+2x+1) I think I could solve it if I knew how they did this operation: From the solution: ' (x^3)/(x^2+2x+1) = (x-2) + (3x+2)/(x+1)^2 ( After long division) Did they use polynomialdivision? x^3: x^2-2X+1= If so, how?

Homework Statement Hi I just have a problem in regards to setting up your partial fractions when doing nonhomogeneous differential equations using Laplace transforms. I’m at the stage of getting the inverse Laplace of: (1-625S^4)/(S^3 (25S^2+1) ) Homework Equations The Attempt...

From a fraction with infinite sum in denominator to partial fractions?? I am currently studying a course on Perturbation Methods and in particular an example considering the following integral \int_{0}^{\frac{\pi}{4}} \frac{d\theta}{\epsilon^2 + \sin^2 \theta}. There's a section of the...

One last question to Integrate x^2/(1+4•x^2). I would assume you would do long division but 4x^2 is bigger than x^2. so would you either pull out a 1/4 and it would be 1/4 ∫ x^2/(1/4+•x^2) dx or would the first term when doing long division be 1/4? or am I just totally wrong and you...

Homework Statement Consider an object that is coasting horizontally subject to a drag force f = -bv = cv^2. Write down Newton's second law... The Attempt at a Solution So I did all of the steps leading up to this: m∫\frac{dv}{bv+cv^2}=-t dt Using partial fractions I get \frac{1}{bv+cv} =...

Homework Statement determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx Homework Equations partial fractions technique The Attempt at a Solution i know it's partial fractions and i thought i did it right but i got the wrong answer. (4x+10)/(9x^2+24x+16) =...

Homework Statement I need to integrate v(t) = V( \frac{1- e^{-2gt/V}}{1+ e^{-2gt/V}}) to show that the position function is given by s(t) = Vt + \frac{V^2}{g}ln(\frac{1 + e^{-2gt/V}}{2}) Homework Equations g is the acceleration due to gravity V is the terminal velocity The Attempt at...

Im reading Lang's first course in calculus and can't understand one step that he does when trying to integrate quotients with quadratic factors in the denominator. He's trying to find the integral of \int{\frac{1}{(x^2+1)^n}dx} but he's first starting with the case where n=1 Then while...

Homework Statement \int\frac{1}{x\sqrt[3]{x+1}}dx (That's a cubic root in the denominator, by the way. Not an x cubed.) The Attempt at a Solution I thought possibly partial fractions, but I've never seen it done with a root in the denominator. Integration by parts was...

hello world, I've been doing some summertime training to brush up my math skills and have been struggling with this [dy]/[/dt]=(4exp(-y)+const*exp(-2y))^1/2 In fact this is the simplified version of a Bernouilli equation. I know that it is separable, I'm just struggling with the...

Homework Statement Use partial fractions to find the sum of the series: \Sigman=1 to infinity \frac{5}{n(n+1)(n+2} Homework Equations Partial Fraction breakdown: \Sigma \frac{5}{2n}+\frac{5}{2(n+2)}+\frac{5}{(n+1)} The Attempt at a Solution When I tried to cancel terms out, it is...

Why in partial fractions does the power of the denominator have to be one more than that of the numerator, when splitting up the expression. Skip to 5:30. Thanks.

Homework Statement ∫10x-2x2/((x-1)2(x+3)) Solve by partial fractions. The Attempt at a Solution ∫A/(x-1) +B/(x-1)2 + C(x+3) after setting up the partial fractions and multiplying each term by LCD: 10x-2x2= A(x-1)(x+3) + B(x+3) + C(x-1)2 10x-2x2= A(x2+2x-3) +Bx+3B +Cx-C 10x-2x2=...

Now yesterday I got help in realizing how to evaluate the sums of certain series, but while doing it I never got the reason behind why we take a series such as: \sum from k=1 to ∞ 1/k(k+3), I know how to solve the sum, but why do we have to convert it to a set of partial fractions in order to do it?

Homework Statement I have this lowpass circuit which I have transformed to the S-domain. The circuit is to be exposed to a unit step, and then I shall convert the transient response to the time domain. Here's the transfer function of the lowpass circuit: H(s) = \frac{\frac{1}{LC}}{s^2 +...

In partial fractions, why \frac{3x+5}{(1-2x)^2} = \frac{A}{(1-2x)^2} + \frac{B}{(1-2x)} and not \frac{3x+5}{(1-2x)^2} = \frac{A}{(1-2x)} + \frac{B}{(1-2x)} Why exists the exponent on the denominator in the right hand side of the equation?

Homework Statement Hi. My first post! I'm trying to solve for where a is a constant: ∫ (x/a)1/2*(x/(x-a)) dx Homework Equations See above The Attempt at a Solution I've tried integration by parts by setting u=(x/a)1/2 but I end up having to solve ∫ (x/a)1/2ln(x-a) - which I...