1. ### A Does this integration have a closed form solution?

I was trying to solve a differential equation that I defined to study the dynamics of a system. Meanwhile, I encounter integration. The integration is shown in the image below. I tried some solutions but I am failed to get a solution. In one solution, I took "x" common from the denominator terms...
2. ### I Equating coefficients of complex exponentials

I have an equation that looks like ##i\dot{\psi_n}=X~\psi_n+\frac{C~\psi_n+D~a~\psi^\ast_{n+1}+E~b~\psi_{n+1}}{1+\beta~(D~\psi^\ast_{n+1}+E~\psi_{n+1})}## where ##E,b,D,a,C,X## are constants. I have the ansatz ##\psi_n=A_n~e^{ixt}+B^\ast_n~e^{-itx^\ast}##, ##x## and ##A_n,B_n## are complex...
3. ### How to get the third value (A), using partial fractions

Homework Statement y(w)= 3/(iw-1)^2(-4+iw) Homework Equations N/A The Attempt at a Solution 3/(iw-1)^2(-4+iw) = A/iw-1 + B/(iw-1)^2 + C/-4+iw for B iw = 1 B=3/-4+1 = -1 for C iw = 4 C= 3/(4-1)^2 = 1/3 I know the answer for A should be -1/3 however I am unsure how to obtain this as if the...
4. ### B Complex Integration By Partial Fractions

Hello, I am enrolled in calculus 2. Just having started a section in our text book about integration by partial fractions, I eagerly began trying to use this integration technique wherever I could. After messing around for multiple days, I ran into this problem: ∫ 1/(x^2+1)dx I immediately...
5. ### Partial Fractions Problem

Homework Statement The question is stated at the top of the attached picture with a solution 20160303_095831.jpg The correct results of the coefficients are A=2, B=-5, C=1 I have tried this problem multiple times and am still getting ugly coefficients. I have no idea why. A fresh pair of eyes...
6. ### Why is my partial fraction decomp. wrong?

Homework Statement Decompose \frac{2(1-2x^2)}{x(1-x^2)} I get A = 2, B =-1, C = 1, but this doesn't recompose into the correct equation, and the calculators for partial fraction decomposition online all agree that it should be A = 2, B = 1, C = 1. Here is one of the online calculator results...
7. ### Very long Taylor expansion/partial fraction decomposition

Homework Statement I want to express the following expression in its Taylor expansion about x = 0: $$F(x) = \frac{x^{15}}{(1-x)(1-x^2)(1-x^3)(1-x^4)(1-x^5)}$$ The Attempt at a Solution First I tried to rewrite the function in partial fractions (its been quite a while since I've last...
8. ### Partial Fractions

Why, when a fraction has repeated linear terms in its denominator e.g. (11x2+14x+5)/[(x+1)2(2x+1)] does it have to be split into three partial fractions, A/(x+1) + B/(x+1)2 + C/(2x+1)? When my first saw this example, my initial reaction was to split it into A/(x+1)2 +B/(2x+1), but after working...