All Questions
11
questions
1
vote
1
answer
124
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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
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
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
1
vote
1
answer
65
views
integral problem $\int \frac{2 \lambda a}{\mathbf{ (e^{at}-1)\lambda \sigma^2+2ae^{-at}}}dt $
Does anybody know how to tackle the below integral? I am analyzing a formula derivation where this appears as the final calculation, but I don't know how to get it solved
$$\int \frac{2 \lambda a}{\...
- 1,137
1
vote
1
answer
54
views
Integration by partial-fractions, I´m stuck in this one.
I don´t really know how get the factors in the denominator which allow me to use a case
$\int\frac{x^2+1}{x^2-x} dx$
- 77
4
votes
4
answers
856
views
How to solve certain types of integrals
I'm asking for a walk through of integrals in the form:
$$\int \frac{a(x)}{b(x)}\,dx$$
where both $a(x)$ and $b(x)$ are polynomials in their lowest terms. For instance $$\int \frac{x^3+2x}{x^2+1}\,dx$...
- 233
3
votes
3
answers
279
views
Partial Fractions - $\frac{x^3}{x^2 + 12x +36}$
Ok, so I know that since the numerator has a higher power that long division is needed. So after doing that, the main fraction is $\frac{-6x-36}{x^2 + 12x + 36}$. I think that's right. But my problem ...
- 267
7
votes
5
answers
378
views
Evaluate $\int{\frac{4x}{(x^2-1)(x-1)}dx}$
So I know I need to use the partial fractions method to solve this integral. However when I split it as:
$$\frac{4x}{(x^2-1)(x-1)} = \frac{Ax + B}{x^2-1} + \frac{C}{x-1}$$
I find that I can't solve ...
- 165