This document contains a table of integrals with 84 entries listing common integral formulas. Each entry gives the integral of a function and its solution. The integrals cover functions involving polynomials, trigonometric functions, hyperbolic functions, logarithms, and others.
Salas, V. (2024) "John of St. Thomas (Poinsot) on the Science of Sacred Theol...Studia Poinsotiana
I Introduction
II Subalternation and Theology
III Theology and Dogmatic Declarations
IV The Mixed Principles of Theology
V Virtual Revelation: The Unity of Theology
VI Theology as a Natural Science
VII Theology’s Certitude
VIII Conclusion
Notes
Bibliography
All the contents are fully attributable to the author, Doctor Victor Salas. Should you wish to get this text republished, get in touch with the author or the editorial committee of the Studia Poinsotiana. Insofar as possible, we will be happy to broker your contact.
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In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.
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Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
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Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
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Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
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Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
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Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
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Heavy metals are naturally occuring metallic chemical elements that have relatively high density, and are toxic at even low concentrations. All toxic metals are termed as heavy metals irrespective of their atomic mass and density, eg. arsenic, lead, mercury, cadmium, thallium, chromium, etc.
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We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
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spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
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genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
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1. Anexo D
Tabla de Integrales
(PUEDE SUMARSE UNA CONSTANTE ARBITRARIA A CADA INTEGRAL)
1.
Z
xn
dx =
1
n + 1
xn+1
(n 6= −1)
2.
Z
1
x
dx = log | x |
3.
Z
ex
dx = ex
4.
Z
ax
dx =
ax
log a
5.
Z
sen x dx = − cos x
6.
Z
cos x dx = sen x
7.
Z
tan x dx = − log |cos x|
8.
Z
cot x dx = log |sen x|
9.
Z
sec x dx = log |sec x + tan x| = log
¯
¯
¯
¯tan
µ
1
2
x +
1
4
π
¶¯
¯
¯
¯
227
2. 228 Tabla de Integrales
10.
Z
csc x dx = log |csc x − cot x| = log
¯
¯
¯
¯tan
1
2
x
¯
¯
¯
¯
11.
Z
arcsen
x
a
dx = x arcsen
x
a
+
√
a2 − x2 (a > 0)
12.
Z
arccos
x
a
dx = x arccos
x
a
−
√
a2 − x2 (a > 0)
13.
Z
arctan
x
a
dx = x arctan
x
a
−
a
2
log
¡
a2
+ x2
¢
(a > 0)
14.
Z
sen2
mx dx =
1
2m
(mx − sen mx cos mx)
15.
Z
cos2
mx dx =
1
2m
(mx + sen mx cos mx)
16.
Z
sec2
x dx = tan x
17.
Z
csc2
x dx = −cot x
18.
Z
senn
x dx = −
senn−1
x cos x
n
+
n − 1
n
Z
senn−2
x dx
19.
Z
cosn
x dx =
cosn−1
x sen x
n
+
n − 1
n
Z
cosn−2
x dx
20.
Z
tann
x dx =
tann−1
x
n − 1
−
Z
tann−2
x dx (n 6= 1)
21.
Z
cotn
x dx =
cotn−1
x
n − 1
−
Z
cotn−2
x dx (n 6= 1)
22.
Z
secn
x dx =
tan x secn−2
x
n − 1
+
n − 2
n − 1
Z
secn−2
x dx (n 6= 1)
23.
Z
cscn
x dx =
cot x csc n−1
x
n − 2
+
n − 2
n − 1
Z
cscn−2
x dx (n 6= 1)
24.
Z
senh x dx = cosh x
25.
Z
cosh x dx = senh x
3. 229
26.
Z
tanh x dx = log |cosh x|
27.
Z
coth x dx = log |sen hx|
28.
Z
sech x dx = arctan (senh x)
29.
Z
csch x dx = log
¯
¯
¯tanh
x
2
¯
¯
¯ = −
1
2
log
cosh x + 1
cosh x − 1
30.
Z
senh2
x dx =
1
4
senh 2x −
1
2
x
31.
Z
cosh2
x dx =
1
4
senh 2x +
1
2
x
32.
Z
sech2
x dx = tanh x
33.
Z
senh−1 x
a
dx = xsenh−1 x
a
−
√
x2 − a2 (a > 0)
34.
Z
cosh−1 x
a
dx =
½
xcosh−1 x
a
−
√
x2 − a2
£
cosh−1
¡x
a
¢
> 0, a > 0
¤
xcosh−1 x
a
+
√
x2 − a2
£
cosh−1
¡x
a
¢
< 0, a > 0
¤
35.
Z
tanh−1 x
a
dx = xtanh−1 x
a
+
a
2
log
¯
¯a2
− x2
¯
¯
36.
Z
1
√
a2 + x2
dx = log
³
x +
√
a2 + x2
´
= sen h−1 x
a
(a > 0)
37.
Z
1
a2 + x2
dx =
1
2
arctan
x
a
(a > 0)
38.
Z √
a2 − x2 dx =
x
2
√
a2 − x2 +
a2
2
arcsen
x
a
(a > 0)
39.
Z
¡
a2
− x2
¢3
2
dx =
x
8
¡
5a2
− 2x2
¢ √
a2 − x2 +
3a4
8
arcsen
x
a
(a > 0)
40.
Z
1
√
a2 − x2
dx = arcsen
x
a
(a > 0)
41.
Z
1
a2 − x2
dx =
1
2a
log
¯
¯
¯
¯
a + x
a − x
¯
¯
¯
¯
4. 230 Tabla de Integrales
42.
Z
1
(a2 − x2)
3
2
dx =
x
a2
√
a2 − x2
43.
Z √
x2 ± a2 dx =
x
2
√
x2 ± a2 ±
a2
2
log
¯
¯
¯x +
√
x2 ± a2
¯
¯
¯
44.
Z
1
√
x2 − a2
dx = log
¯
¯
¯x +
√
x2 − a2
¯
¯
¯ = cosh−1 x
a
(a > 0)
45.
Z
1
x(a + bx)
dx =
1
a
log
¯
¯
¯
¯
x
a + bx
¯
¯
¯
¯
46.
Z
x
√
a + bx dx =
2 (3bx − 2a) (a + bx)
3
2
15b2
47.
Z √
a + bx
x
dx = 2
√
a + bx + a
Z
1
x
√
a + bx
dx
48.
Z
x
√
a + bx
dx =
2 (bx − 2a)
√
a + bx
3b2
49.
Z
1
x
√
a + bx
dx =
1
√
a
log
¯
¯
¯
√
a+bx−
√
a
√
a+bx+
√
a
¯
¯
¯ (a > 0)
2
√
−a
arctan
q
a+bx
−a
(a > 0)
50.
Z √
a2 − x2
x
dx =
√
a2 − x2 − a log
¯
¯
¯
¯
a +
√
a2 − x2
x
¯
¯
¯
¯
51.
Z
x
√
a2 − x2 dx = −
1
3
¡
a2
− x2
¢3
2
52.
Z
x2
√
a2 − x2 dx =
x
8
¡
2x2
− a2
¢ √
a2 − x2 +
a4
8
arcsen
x
a
(a > 0)
53.
Z
1
x
√
a2 − x2
dx = −
1
a
log
¯
¯
¯
¯
a +
√
a2 − x2
x
¯
¯
¯
¯
54.
Z
x
√
a2 − x2
dx = −
√
a2 − x2
55.
Z
x2
√
a2 − x2
dx = −
x
2
√
a2 − x2 +
a2
2
arcsen
x
a
(a > 0)
56.
Z √
x2 + a2
x
dx =
√
x2 + a2 − a log
¯
¯
¯
¯
¯
a +
√
x2 + a2
x
¯
¯
¯
¯
¯
5. 231
57.
Z √
x2 − a2
x
dx =
√
x2 − a2 − a arccos
a
| x |
=
√
x2 − a2 − arcsec
³x
a
´
(a > 0)
58.
Z
x
√
x2 ± a2 dx =
1
3
¡
x2
± a2
¢3
2
59.
Z
1
x
√
x2 + a2
dx =
1
a
log
¯
¯
¯
¯
x
a +
√
x2 + a2
¯
¯
¯
¯
60.
Z
1
x
√
x2 − a2
dx =
1
a
arccos
a
| x |
(a > 0)
61.
Z
1
x2
√
x2 ± a2
dx = ±
√
x2 ± a2
a2x
62.
Z
x
√
x2 ± a2
dx =
√
x2 ± a2
63.
Z
1
ax2 + bx + c
dx =
(
1
√
b2−4ac
log
¯
¯
¯2ax+b−
√
b2−4ac
2ax+b+
√
b2−4ac
¯
¯
¯ (b2
> 4ac)
2
√
4ac−b2 arctan 2ax+b
√
4ac−b2 (b2
< 4ac)
64.
Z
x
ax2 + bx + c
dx =
1
2a
log
¯
¯ax2
+ bx + c
¯
¯ −
b
2a
Z
1
ax2 + bx + c
dx
65.
Z
1
√
ax2 + bx + c
dx =
(
1
√
a
log |2ax + b + 2
√
a
√
ax2 + bx + c| (a > 0)
1
√
−a
arcsen −2ax−b
√
b2−4ac
(a < 0)
66.
Z √
ax2 + bx + c dx =
2ax + b
4a
√
ax2 + bx + c +
4ac − b2
8a
Z
1
√
ax2 + b + c
dx
67.
Z
x
√
ax2 + bx + c
dx =
√
ax2 + bx + c
a
−
b
2a
Z
1
√
ax2 + bx + c
dx
68.
Z
1
x
√
ax2 + bx + c
dx =
(
−1
√
c
log
¯
¯
¯
2
√
c
√
ax2+bx+c+bx+2c
x
¯
¯
¯ (c > 0)
1
√
−c
arcsen bx+2c
|x|
√
b2−4ac
(c < 0)
69.
Z
x3
√
x2 + a2 dx =
µ
1
5
x2
−
2
15
a2
¶ q
(a2 + x2)3
70.
Z √
x2 ± a2
x4
dx =
∓
q
(x2 ± a2)3
3a2x3
71.
Z
sen ax sen bx dx =
sen(a − b)x
2(a − b)
−
sen(a + b)x
2(a + b)
¡
a2
6= b2
¢
6. 232 Tabla de Integrales
72.
Z
sen ax cos bx dx =
cos(a − b)x
2(a − b)
−
cos(a + b)x
2(a + b)
¡
a2
6= b2
¢
73.
Z
cos ax cos bx dx =
sen(a − b)x
2(a − b)
−
sen(a + b)x
2(a + b)
¡
a2
6= b2
¢
74.
Z
sec x tan x dx = sec x
75.
Z
csc x cot x dx = −csc x
76.
Z
cosm
x senn
x dx =
cosm−1
x senn−1
+x
m + n
+
m − 1
m + n
Z
cosm−2
x senn
x dx =
= −
senn−1
x cosm+1
x
m + n
+
n − 1
m + n
Z
cosm
x senn−2
x dx
77.
Z
xn
sen ax dx = −
1
a
xn
cos ax +
n
a
Z
xn−1
cos ax dx
78.
Z
xn
cos ax dx =
1
a
xn
sen ax −
n
a
Z
xn−1
sen ax dx
79.
Z
xn
eax
dx =
xn
eax
a
−
n
a
Z
xn−1
eax
dx
80.
Z
xn
log(ax) dx = xn+1
·
log ax
n + 1
−
1
(n + 1)2
¸
81.
Z
xn
(log ax)m
dx =
xn+1
n + 1
(log ax)m
−
m
n + 1
Z
xn
(log ax)m−1
dx
82.
Z
eax
sen bx dx =
eax
(a sen bx − b cos bx)
a2 + b2
83.
Z
eax
cos bx dx =
eax
(b sen bx + a cos bx)
a2 + b2
84.
Z
sech x tanh x dx = −sech x
85.
Z
csch x coth x dx = −csch x