Partial fractions Definition and 298 Threads

Homework Statement integral of: 1/(((L2)/4)+y2)This is for proving the flux through a cube from a wire going through it is = Qenc/epsilon0 All that's left for one face after taking out constants is the above equation, and I really don't want to go re learn how to do partial fractions again...

Homework Statement dx/dt=3x(x-5); x(0)=2 Homework Equations dx/dt=F(x)G(t) dx/dt=x' The Attempt at a Solution First I separated the variables using F=3x(x-5) and G=3 x'/(3x(x-5))=3 Applying method of quadrature: \int\frac{x'}{(3x(x-5)}dt=\int3 dt On the right hand...

We were discussing them in my math methods class today however I'm not really sure how the idea works. Does anyone know of any online references that might be of some help? Google wasn't much help for me =/

Homework Statement Evaluate the integral: \int_{1}^2 \frac{4y^2 - 7y -12}{y(y+2)(y-3)}dy Homework Equations None. The Attempt at a Solution \frac{4y^2 -7y -12}{y(y+2)(y-3)} = \frac{A}{y} + \frac{B}{y+2} + \frac{D}{y-3} y = 0: -12 = -6A \rightarrow A=2 y = -2: 16 + 14 -...

Homework Statement It's hard to explain, I can do everything exept get the answer to what I'v pointed out below. I just don't know what order to solve it into get the correct answer, I must have tried every method except the right one! Homework Equations The Attempt at a...

Use partial fractions to integrate x^3/(x^3+1)The Attempt at a Solution \int x^{3}/(x^{3}+1) dx Homework Statement Homework Equations The Attempt at a Solution \int x^{3}/x^{3}+1 dx I know that first i have to perform long division but i am at a loss how to do this THanks

Homework Statement \int\frac{e^xcos(log_7(e^x+9))}{(e^x+9)ln(7)}dx Homework Equations The Attempt at a Solution Let u= (ex+9) du= exdx New integral \int\frac{cos(log_7(u))}{(u)ln(7)}du This is where I got l little lost. Should I let log7(u)=\frac{ln(u)}{ln(7)}? Or is this...

Suppose that q(z) = 1, and p(z) = (1 + z)(1 + 3z). We wish to express q(z)/p(z) in the form where A and B are constants. To find them, we multiply through by p(z) = (1 + z)(1 + 3z) and obtain 1 = A(1 + 3z) + B(1 + z) = (A + B) + (3A + B)z Im fine up to this point, But according to...

Homework Statement \int(3x3-4x2-3x+2)/(x4-x2) Homework Equations P(x)/Q(x)=A1/(x-r1)+A2/(x-r2)+... if x-r occurs with multiplicity m, then A/(x-r) must be replaced by a sum of the form: B1/(x-r)+B2/(x-r)2+... I think this second equation is the source of my confusion. The Attempt at a...

1.\int2x^2+x+9/(9x+1)(x^2+9) dx 2. (A/9x+1) + [(Bx + C ) / (x^2 + 9)] I get the worst numbers when I solve the system. The question is from an old exam and calculators are not allowed. Am I doing something wrong or is there another way to integrate this?

Hello! Quick question reagrding partial fractions. When there is a factor such as (x+2)3 in the denominator, then the fraction is separated into the components (x+2)1+...+(x+2)3. I am not convinced I understand quite why this is so. Partial fractions guides all offer something on the theme...

Homework Statement The question asks me to express the integrand in partial fractions to evaluate the integral \int \frac{13x-4}{6x^{2} -x -2} dx Homework Equations The Attempt at a Solution Well 6x² -x - 2 doesn't factorise (or I can't see it factorised). So I tried...

Homework Statement Hi, \int \frac{1}{x(x^{2}+1)}dx Homework Equations The Attempt at a Solution well I split this into partial fractions \frac{A}{x} + \frac{Bx + C}{x^{2} + 1} so 1 \equiv A(x^{2}+1) + (Bx + C)x when x = 0, A =1 when x = 1, Bx + C = -1 so...

Hello, I'm don't understand a step in the following integral: ∫(x-1)/(2x+1)dx = ∫(1/2)dx − (3/2)∫1/(2x+1)dx = (1/2)x − (3/4)ln|2x+1| + C The first step, where you get the 2 integrals ∫(1/2)dx and -(3/2)∫1/(2x+1)dx Where do (1/2)dx and -(3/2) come from? And where does (3/4) come...

Homework Statement Need to refresh my memory :-S Indefinite integral of x/(1+x^2) .. Homework Equations The Attempt at a Solution Would I use partial fractions on that bad boy?

\int \frac{2x+1}{4x^2+12x-7}dx \frac{1}{4} \int \frac{2x+1}{x^2+3x-\frac{7}{4}}dx \frac{1}{4} \int \frac{2x+1}{(x+\frac{3}{2})^2-4}dx u=x+\frac{3}{2} \frac{1}{2} \int \frac{u-1}{u^2-4}du \frac{1}{2} \int \frac{u}{u^2-4}du -\frac{1}{2}\int \frac{du}{u^2-4} \frac{1}{4}...

Homework Statement \int \sqrt{tanx} dx The Attempt at a Solution I used the substitution u = sqrt(tanx), then x = arctan(x^2) so: 2 \int \frac{u^{2}}{u^{4} + 1} du = 2 \int \frac{u^{2}}{(u^{2} + 1)^{2} - 2u^{2}} =2 \int \frac{u^{2}}{(u^2 -\sqrt{2}u + 1)(u^2 +\sqrt{2}u + 1)} now...

Partial fractions of (-2x2+10x+8)/[x2(x+2)] I initally thought that it was A/x + Bx+C/x2 + D/x+2 but you really just do Ax+B/x2 + C/x+2 ...can anyone explain why the "x2" isn't split?

I'm trying to do a question that requires the expansion of the following using partial fractions: f(z)=\frac{1}{(1+z^3)^2}. The fact that the bottom is squared is throwing me off for some reason... I've factorized the bottom, but I'm not sure whether I should use the complex roots or not, or...

Hi, had to learn partial fractions last year for laplace transforms, but have forgotten the general rules, and now i can't work out how to turn this into partial fractions: \frac{s}{\left(s^{2}+4\right)\left(s^{2}+9\right)}...

Homework Statement This problem is killing me. I need to bust this thing up using partial fractions. Homework EquationsThe Attempt at a Solution I'm leaning towards it being separated like this. Is this correct? If it is, I'm not exactly sure what I'm supposed to do next.

Homework Statement Sorry I don't have equation editor working 1/(z+1)(z2 + 2z + 2) Homework Equations The Attempt at a Solution (z2 + 2z + 2) z2 + 1) can be factor as (z - i)(z + i) However, I'm having trouble seeing the pattern on what (z2 + 2z + 2) would become, I...

how do you integrate 1/(x2 + 1)2 ? i have tried integration by partial fractions but when you set 1 equal to (Ax +B)(x2+1) + (Cx + D) this leads to A=B=C=0 and D=1 which just gives you the original equation

Hi Can anybody help me with these 3 problems?: 1) Express (3x-1)/(x+3)^2 in the form A/(x+3) + B/((X+3)^2) where A and B are constants. 2) A curve C has parametric equations: x=cost and y=2-cos2t (between 0 and pi) a)prove this can be expressed as the cartesian equation y=3-2x^2 b)...

I'm sure this is a no brainer to someone, but here it is.. what is does the partial fraction of this look like in expanded form? Or how can I make it fit on the table of laplace transforms? __(2s+1)__ (s-1)^2 + 1

Homework Statement I need to integrate this using partial fractions. "b/(x^2-a^2)" Homework Equations The Attempt at a Solution I have no idea where to begin.

Integration with partial fractions -- help! Homework Statement Here is the problem: http://img130.imageshack.us/img130/1673/integralthing.png The answer should be 4. Homework Equations N/A The Attempt at a Solution Here are my steps so far: (5x^2 - 17x + 10) / ((x-1)^3 *...

Homework Statement \int \frac{xdx}{x^3-1} Homework Equations The Attempt at a Solution Having difficulties with this one. I managed to break it down to two partial fractions, being x-1 and x^2+x+1 but couldn't make anything out of it.

Homework Statement Integral(sinx(x)dx/(cos^2(x)+cos(x)-2) Homework Equations The Attempt at a Solution What I tried to do first was factor the denominator, so i got (cos(x)-1)(cos(x)+2) from there, I set up my partial fractions equation trying to solve B(cos(x)-1) + A(cos(x)+2) =...

Homework Statement expand by partial fractions: Homework Equations 2(s+5)/(1.25*s^2+3s+9) The Attempt at a Solution ok I initially used the quadratic formula to get the two roots for the denominator these being (s+6/5+12i/5)(s+6/5-12i/5) i.e complex numbers so now the partial fractions...

\int \frac{5x^2+11x+17}{x^3+5x^2+4x+20}dx \int \frac{5x^2+11x+17}{(x^2+4)(x+5)}dx \frac{Ax+B}{x^2+4}+\frac{C}{x+5}=\frac{5x^2+11x+17}{(x^2+4)(x+5)} (Ax+B)(x+5)+C(x^2+4)=5x^2+11x+17 Ax^2+5Ax+Bx+5B+Cx^2+4C=5x^2+11x+17 x^2(A+C)+x(5A+B)+(5B+4C)=5x^2+11x+17 A+C=5...

\int \frac{x^2+3x+1}{x^4+5x^2+4} (Ax+B)(x^2+1)+(Cx+D)(x^2+4) letting x=0 ..B+4D=1 not sure of the next move

\int \frac{x^3+6x^2+3x+16}{x^3+4x} dx \int \frac{x^3+6x^2+3x+16}{x(x^2+4)} dx \frac{x^3+6x^2+3x+16}{x(x^2+4)}=\frac{A}{x}+\frac{Bx+C}{x^2+4} x^3+6x^2+3x+16=A(x^2+4)+(Bx+C)x x^3+6x^2+3x+16=Ax^2+4A+Bx^2+Cx comparing coefficients.. A+B=6 , C=3 , A=4...

Homework Statement \frac{dP}{dt}=P-P^{2} It seems that Partial Fractions should be used to solve this D.E., but I cannot find an example to go by. I even tried to rewrite the equation as: \frac{d}{dx}Y\left(x\right)=Y\left(x\right)-Y\left(x\right)^{2} But, that isn't helping me...

Homework Statement Compute the integral: int ((1-x^2)/(x^3+x)) dx Homework Equations int ((1-x^2)/(x^3+x)) dx The Attempt at a Solution I think I should use the partial fraction method to simplify the fraction so (1-x^2)/(x^3+x)= A/x + B/ (1+x^2) Therefore...

1/(x+5)^2 (x-1) B=(-1/6) C=(1/36) I can't find the value of A, what method do you use to find it?

Here's (what I think is) a step in partial fractions that I don't understand: http://apthtml.com/images/partialfrac.png I'm taking the regular partial fractions steps and I keep ending up with 1 / (1 - x) rather than 1 / (x - 1). What am I doing wrong?

Hello :smile: I've been stuck on this question for almost 3 hours now, and I still have no idea what to do. We haven't done a question like this in class, although we have done integration with partial fractions. Homework Statement Evaluate...

Homework Statement I need to integrate (2x-5)/(x^2+5x+11) Homework Equations The Attempt at a Solution My problem is just finding a formula for an irreducable quadratic. I know if the denominator was x(x^2+1), I would use A/x+(Bx+C)/(x^2+1). I just don't know the formula in this...

The problem is: ((x^3)+x)/(x-1) And i need to break it into partial fractions... I tried long division and got: ((x^2) +x ) But the book gives me the answer of: (x^2)+x+2+(2/(x-1)) Any help would be very much appreciated, thanks.

Homework Statement Verify that, for all positive values of n, 1/(n+2)(2n+3) -1/((n+3)(2n+5))=(4n+9)/((n+2)(n+3)(2n+3)(2n+5)) For the series ∑_(n=0)^N▒(4n+9)/((n+2)(n+3)(2n+3)(2n+5)) Find The sum to N terms, The sum to infinity. Homework Equations no The Attempt at a...

Homework Statement I((3x^2+x+4)/(x^4+3x^2+2),x) I((3x^2+x+4)/((x^2+1)(x^2+2)),x) I(3x^2/((x^2+1)(x^2+2)),x)+I((x+4)/((x^2+1)(x^2+2)),x) from here i have used partial fractions with no luck Homework Equations The Attempt at a Solution

Homework Statement partial fractions (-x^2+x+3)/((x-2)^2(x+1)) = A/(x-2) + B/((x-2)^2) + C/(x+1) is my partial fractions set up right A= -1/9 B = 1/3 C=1/9

I'm having trouble understanding what the numerator needs to be in the partial fractions. e.g. \frac{1}{(x-1)(x-2)^2}\equiv \frac{A}{x-1}+\frac{Bx+C}{(x-2)^2} Notice how the first numerator has a constant A, while the second is linear Bx+C. Actually... just now I think I may understand...

Hey guys, I have a quick question concerning partial fractions, say i have the values A(..)+B(..)+C(..) and i can only get A b substituting a value for x, but I can not make A or C go zero or A and B go to zero at the same time, if you understand ? How do I get the values B and C ? I remember...

Is it possible to use partial fractions on exponential factors? An expression like this for example... 3^x ______________________ (2^x + 3^x)(5^x + 6^x) Would it break down into something like this? A^x/(2^x + 3^x) + B^x/(5^x + 6^x) What are the rules for repeated factors...

Homework Statement I need to intergrate the following (4x2+2x-1)/ (x3+x2) How to set up problem using linear factors? The Attempt at a Solution Factoring the denominator I get: x2(x+1) By linear/quadratic factoring I get: A/x + Bx+C/ x2 + d/(x+1) Is this right?

Homework Statement use the method of partial fractions on \int \frac{36}{(x-2)(x-1)^2(x+1)^2} dx [b]2. Homework Equations [b]3. The Attempt at a Solution \frac{A}{(x-2)} + \frac{B}{(x-1)} + \frac{C}{(x-1)^2} + \frac{D}{(x+1)} + \frac{E}{(x+1)^2} I took the 36 out of the...

Homework Statement ∫1/[(x+a)(x+b)]dx answer is 1/(a-b) ln[(x+b)/(x+a)] + C Homework Equations The Attempt at a Solution 1=A/(x+a) + B/(x+b) 1=B(x+a) + A(x+b) 1=Bx+ Ba + Ax +Ab so 0=Bx+ Ax, 1=Ba+Ab A=-B, 1=B(a-b) ∫-1/(x+a) +∫1/(x+b) Im not sure if I am headed in...

Homework Statement Integrate: (x-1) / (X^2 - 4x +5) The attempt at a solution Normally I would try to factor this into something like (x-1) (x+3) (That's an example completely unrelated to this problem.) However, as no easy factors quickly occurred to me I did a run through of the...