All Questions
27
questions
1
vote
0
answers
30
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Partial fractions with a repeated factor [duplicate]
I am looking to find a derivation, or a intuitive explanation as for why a partial fraction with a repeated factor needs to include a factor in the expansion for each power possible. How does one ...
- 855
0
votes
3
answers
190
views
Partial Fractions Decomposition-Unsure Which Method To Use When
So I was working on this problem and could not use the cover up method to solve it. I was getting the wrong answer.
Find B.
$$\frac{1}{s^2(s^2+4)}=\frac{A}{s}+\frac{B}{s^2}+\frac{Cs+D}{s^2+4}$$
$$s=0: ...
- 53
1
vote
1
answer
124
views
Which integrating technique should I use?
Just some context: In the mathematical course, I have undertaken this year, I've just learnt how to integrate using partial fractions, substitution(not trig though, just a variable) and integrating ...
- 1,190
0
votes
2
answers
106
views
Solution to $\int\frac{\ln(1+x^2)}{x^2}dx$
Q: $\int\frac{\ln(1+x^2)}{x^2}dx$
Here is my entire working:
So, overall, I started with the reverse product rule, then onto reverse chain rule and then tried to partial fraction, however, I still ...
- 1,190
2
votes
0
answers
299
views
Are there applications of partial fraction decomposition ( of a rational function) outside integration problems?
I've been recently acquainted with a well known technique called " partial fraction decomposition" which allows, for example to express $\frac {x} {x^2-1}$ as $\frac {1}{2(x+1)} + \frac {1} ...
- 1,796
2
votes
1
answer
597
views
Why do some partial fractions have x or a variable in the numerator and others don't?
Why do rational expressions like $\left(\frac{1}{(x-2)^3}\right)$ do not have x in the numerator of the partial fraction but a rational expression like $\left(\frac{1}{(x^2+2x+3)^2}\right)$ does have ...
1
vote
1
answer
81
views
Arbitrarily long decomposition into partial fractions.
$$\int \frac{dx}{x(x+p)(x+2p)(x+3p)...(x+(n-1)p)}= ?$$
I'm trying to solve this integral, and as I usually do in these cases, I break the expression into partial fractions, but I find this case ...
1
vote
1
answer
209
views
Reasoning behind the resolution of partial fractions when denominator is the product of linear factors where some of them are repeating
The following text is from Mathematics for Class XII by Dr. R.D.Sharma, chapter "Indefinite Integrals", topic "Integration of Rational Algebraic Functions by using Partial Fractions&...
- 1,826
0
votes
1
answer
94
views
Partial fractions Integration - Distributing Coefficients
Given the following Integral
$\int \frac{2x^3+ 2x^2+ 2x+ 1}{x^2 (x^2+1)}$
I would expand my fractions like the following
$\frac{A}{x} + \frac{B}{x^2}+\frac{Cx+D}{x^2+1}$
When I look at the ...
- 3
1
vote
3
answers
253
views
Integrating quadratics in denominator
I'm following a book on Calculus that introduces partial fraction expansion. They discuss common outcomes of the partial fraction expansion, for example that we are left with an integral of the form:
...
- 2,493
0
votes
1
answer
912
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Confusion about "picking values of $x$", partial fraction decomposition
One of the methods of decomposing a fraction and finding the constants, $A, B, C,$ etc., is to "pick values of $x$". For example, to find $A$ and $B$ of $${{3x}\over(x-1)(x+2)} = {A\over(x-1)} + {B\...
- 945
0
votes
0
answers
70
views
Mistake in the computation via partial fractions
This is a computation made in Titchmash's Introduction to Zeta functions. I was trying to reverse the computation. However, I kept missing factors.
Consider $\frac{1- xyz^2}{(1-z)(1-xz)(1-yz)(1-xyz)}...
- 8,550
1
vote
3
answers
121
views
Partial Fraction problem solution deviates from the Rule
Question:
Compute $\displaystyle \int\frac{x^2+1}{(x^2+2)(x+1)} \, dx$
My Approach:
As per my knowledge this integral can be divided in partial Fraction of form $\dfrac{Ax+B}{x^2+px+q}$ and then do ...
user517784
0
votes
1
answer
64
views
Polynom and decomposition
I need to know I can decompose into simple elements
$$\frac X{(X+1)^4 (X^2 +1)}$$
What is the easiest way?
2
votes
2
answers
50
views
Calculus 2: Partial fractions problem. Finding the value of a constant
I encountered the following problem.
Let $f(x)$ be a quadratic function such that $f(0) = -6$ and
$$\int \frac{f(x)}{x^2(x-3)^8} dx $$
is a rational function.
Determine the value of $f'(0)$
Here'...
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