All Questions
Tagged with mathematica integration
72
questions
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Logarithmic Function Calculation in Mathematica
I find these results in the evaluation of the logarithms that only differ in the sign $-$ I do not understand why in the first case $\operatorname{Log}[x+1]/8$ is not returned as an answer.
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52
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Difficulty in computing integral
I am currently struggling with computing the following integral (as a whole). First, I define the following function.
\begin{equation}
f(q) = \frac{840q + 190 q^3 + 93 q^5 - 15\sqrt{4+q^2}(28+4q^2 + ...
- 257
2
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1
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111
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Asymptotic analysis for integrals
I am a physics student doing some integrals of the form
$$\lim_{\rho\to\infty} \int dx \int dy \text{ }f(x,y) e^{-\rho (x y)^{3/2}}$$ with $x,y \geq 0$, and $f(x,y)$ is a polynomial ($a_0+a_{x1} x + ...
- 23
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regularized incomplete beta function integration
Solve $\int_{0}^{1}\frac{I_{u^{\frac{1}{p}}}\left ( p+\frac{1}{a} ,1-\frac{1}{a}\right )}{u}du$ . In Mathematica, this integral does not converge but from an article, I got the answer to this integral ...
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Integral of Dirac Delta Derivative Times Non-Smooth Function
I know that if we have some function f(y) that is smooth and has compact support, we get the following by using integration by parts.
$\int f(y) \delta '(y-x) dy = -\int f'(y) \delta (y-x) dy =-f'(x)$
...
- 157
1
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2
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72
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Having trouble with the integral of the second derivative of the function $e^{\frac{-1}{1 - x^2}}$ after a change of variables
The first thing I have to note is that I am not 100% sure whether this problem is due to Mathematica or just the mathematics I have produced. Thus feel free to direct me to the appropriate forum.
Let $...
- 1,030
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Why is this integration finite?
Consider $$\int_{2}^{2+\epsilon}\frac{1}{x^2-2^2}dx=\left.\frac{1}{4}\ln\left|\frac{x-2}{x+2}\right|\right|_2^{2+\epsilon}=\frac{1}{4}\left[\ln\left(\frac{\epsilon}{4+\epsilon}\right)-\lim\limits_{x\...
- 33
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Integration invlolving gaussian kernel
I have been trying to solve this integration . I have tried via changing the coordinate system to cartesian coordinates system but it gets complicated. The integration is
$$\int\limits_{0}^{2\pi}\int\...
- 1
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please help me with mathlab code or mathematical of the integration of this vibrational partition function shown below to arrive at the answer
I want the code to integrate equation(1) or (2)over the limits using mathematical or mathlab to get equation (3) as the answer of Z vibrational partition function , giving the following additional ...
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Numerically integrating $\int_{20}^\infty\frac{4^{1+4ix}\Gamma(-4ix)e^{-2ix}}{(-2i)^{-4ix}}dx$
I want to compute the following integral numerically in Mathematica,
$$\int_{20}^{\infty} \frac{4^{1+4ix}\Gamma(-4ix)e^{-2ix}}{(-2i)^{-4ix}}dx$$
The problem is that when evaluate the integral from $20$...
- 31
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39
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Gaussian Integral like $\exp{[-r^2 - r_\alpha^2 +2 r r_\alpha \cos{(\theta-\theta_\alpha)}]}[r -r_\alpha \cos{(\theta-\theta_\alpha)}]f(r,\theta)$
I have a Gaussian kernel that I wish to evaluate $$\int_{0}^{\infty} \int_{0}^{2\pi} \exp{[-r^2 - r_\alpha^2 +2 r r_\alpha \cos{(\theta-\theta_\alpha)}]} [r -r_\alpha \cos{(\theta-\theta_\alpha)}]f(r,\...
- 11
3
votes
1
answer
112
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Cauchy's theorem and mathematica disagree? Integral involving branch points.
Consider the following integral:
$$\int_{-\infty}^{\infty} \frac{dx}{\sqrt{x^2-2i\epsilon x -1}(x^2+1)}$$
where $\epsilon$ is an infinitesimal positive number. In the complex $x$-plane, the integrand ...
- 3,968
1
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76
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Derivation of an integral that generates a Bessel function of the second kind
I am working with a function where I need to solve an integral of the following form:
where $K$ is a modified Bessel function of the second kind. The image is from "Integrals and Series: Volume ...
- 61
1
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3
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Integrating $\int_0^\infty \frac{x^n}{e^x+1} \,dx$, where $n$ is an integer
If the general case is too hard for some reason, I mostly need the $n=2$ case of the following integral:
$$ \int_0^\infty \frac{x^n}{e^x+1} \,dx $$
For some reason Mathematica fails me, as it claims ...
- 61
7
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3
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229
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General formula for $\int^1_0 x^\alpha \log(1-x)\operatorname{Li}_2 (x)\, \mathrm dx$
Consider a following definite integral
$$I(\alpha) = \int^1_0 x^\alpha \log(1-x)\operatorname{Li}_2 (x)\, \mathrm dx$$
Mathematica is able to provide a result for many $\alpha$ integers. See table ...
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