Graceli Table of integrals for a system where it replaces the variable C and PI by a series of decim

in integral calculus have pi or a constant C, and the infinitesimal calculus Graceli integral formulas are the same, but the constants pi and C are replaced by series or series summation or multiplication of series, potentiation series, logarithms, divisions of series or even series of subtractions, and even a house of decimals to be achieved as it asks equation.

no cálculo integral temos o pi ou uma constante C, sendo que no cálculo Graceli infinitesimal integral sao as mesmas fórmulas, mas as constantes pi e C são substituidas pela série, ou somatória de séries, ou multiplicação de séries, potencialização de séries, logaritimos, divisões de séries, ou mesmo subtrações de séries, e mesmo numa casa de decimais a ser alcançada conforme se pede a equação.

The infinite, the finite limit and the series system Graceli series .

The finite and the infinite system Graceli .

The limit system graceli have finite .

And in the infinite system graceli have :

And the series elevated the n ... times have the infinite within series within series .

Geometry Graceli series of infinitesimal waves to peaks and troughs .

Infinitesimal Graceli series .

Author ; Ancelmo Luiz Graceli .

Series and cells and gaps infinitesimal .

Limit system Graceli .
Where the part divided by the whole leads to the result x , and divided by the whole will always be lower between 1 and greater than zero . And the result is g .

Series averages infinitesimal .

With this we sums of equation y , z, ... c n divided by the whole of each equation for y , z and c , n .... with this we have series of summations of equations and equalization [ average series ] between them .

Gaps between infinitesimal , which is divided into 1 second, third , n ... infinitesimal .

Where the result g becomes the first series and gap, oh another gap further . Thus gradually .

G divided by t = 1 i1 infinitesimal .
H divided by the result of g and t [ i1 ] = i2 .

Thus, successively .
4/8 = 0.5 0.5 / 8 = i1 .

I1 / t = h . thus successively formed series infinitesimal .

Thus , we have results for sums , multiplication , fractions , potentiation , proportionalities series of infinitesimal Graceli .

for example range from 1 to 9 .

Where in each series has always values in a number smaller than one digit in the series following proportion to the ninth .

So have results for each grade , and the sum of all until the ninth . Or even a few pairs or odd according to the equation so requires . Ie after the result they are divisible from last to first , ie , from ninth to first .

Geometry Graceli series of infinitesimal waves to peaks and troughs .

With the series being raised to the successive peaks and troughs forms a geometric irregularities or depressions progressive increasing or decreasing , or even a row with each other.

In the micro world and even quantum flows and the smallest we have is not a straight and perfect curves or , rather, peaks and troughs within the lines and curves .

The shortest distance between two points for an infinitesimal geometry is a depression or a peak .

The shortest distance between two points that are closest in distance is a diametrical formed in series inside diameters diameters, such as layers of onion, so indefinitely.

Ie , a universe of diametric series is impossible to know what is the distance and its final form . Or distance and so be on the limit infinitesimal .

Thus , the minimum distance between two points is the infinitesimal layers of each diametrical extent by which they may be closer .

That is, each point in issue to be addressed .

Ie , it is like an onion layers under layers .

Where the whole subtracted or divided part , has an outcome x , and the result goes aser divided the whole. Thus , infinitely .

Theory Graceli limit .
-OR LG = T / P = x
x / t = g .

subtracted from the whole or split the part where the result of the whole is divided .

And being elevated to several subdivisions have sets limits within limits in decimal irrational divisible .

Where we have g = li , l2/l1 / l3 / 2 n .....

Ie we have series infinitesimal graceli within limits graceli .

DF / dx [ ln ... x ] = f ¨ [ xln ... ]

Statistics and potentials in system Graceli series .
The limits may be raised to Graceli reasons of uncertainties and improbabilities , and statistics when a high potential .

Graceli Table of integrals for a system where it replaces the variable C and PI by a series of decimal Graceli limit or the sum or division , or multiplication of some series .

With this we have the integral calculus to Graceli series .

Funções Racionais[editar]

Ver artigo principal: Anexo:Lista de integrais de funções racionais

$\int x^n\,dx = \frac{x^{n+1}}{n+1} + C\qquad\mbox{ para }n \ne -1$
$\int \frac{1}{x}\,dx = \ln{\left|x\right|} + C$
$\int \frac{1}{a^2+x^2} \, dx = \frac{1} {a} arctan({x}/{a}) + C$

Logaritmos[editar]

Ver artigo principal: Anexo:Lista de integrais de funções logarítmicas

$\int \log_a x\,dx = x\log_a x - \frac{x}{\ln a} + C$
$\int \ln x\,dx = x (\ln x - 1) + C$

Funções Exponenciais[editar]

Ver artigo principal: Anexo:Lista de integrais de funções exponenciais

- Caso particular: $a = e, \int e^x\,dx = e^x + C$

Funções Irracionais[editar]

Ver artigo principal: Anexo:Lista de integrais de funções irracionais

- Caso particular: $a = 1, \int {1 \over \sqrt{1-x^2}}\, dx = \arcsin {x} + C$
- Caso particular: $a = 1, \int {-1 \over \sqrt{1-x^2}} \, dx = \arccos {x} + C$

Funções Trigonométricas[editar]

Ver artigo principal: Anexo:Lista de integrais de funções trigonométricas

$\int \cos{x} \, dx = \sin{x} + C$
$\int \sin{x} \, dx = -\cos{x} + C$
$\int \tan{x} \, dx = -\ln{\left| \cos {x} \right|} + C$
$\int \csc{x} \, dx = \ln{\left| \csc{x} - \cot{x}\right|} + C$
$\int \sec{x} \, dx = \ln{\left| \sec{x} + \tan{x}\right|} + C$
$\int \cot{x} \, dx = \ln{\left| \sin{x} \right|} + C$
$\int \sec{x} \tan{x} \, dx = \sec {x} + C$
$\int \csc{x} \cot{x} \, dx = -\csc {x} + C$
$\int \sec^2 x \, dx = \tan x + C$
$\int \csc^2 x \, dx = -\cot x + C$
$\int \sin^2 x \, dx = \frac{1}{2}(x - \sin x \cos x) + C$
$\int \cos^2 x \, dx = \frac{1}{2}(x + \sin x \cos x) + C$

Funções Hiperbólicas[editar]

Ver artigo principal: Anexo:Lista de integrais de funções hiperbólicas

$\int \sinh x \, dx = \cosh x + C$
$\int \cosh x \, dx = \sinh x + C$
$\int \tanh x \, dx = \ln (\cosh x) + C$
$\int \mbox{csch}\,x \, dx = \ln\left| \tanh {x \over2}\right| + C$
$\int \mbox{sech}\,x \, dx = \arctan(\sinh x) + C = \arcsin(\tanh(x)) + C = 2\arctan(\exp(x)) + C$
$\int \coth x \, dx = \ln|\sinh x| + C$

Integrais Definidas[editar]

Existem funções cujas antiderivadas não podem ser expressas de forma fechada. No entanto, os valores das integrais definidas dessas funções em intervalos comuns podem ser calculados. Algumas integrais definidas de uso frequente estão relacionadas abaixo.

$\int_0^\infty{\sqrt{x}\,e^{-x}\,dx} = \frac{1}{2}\sqrt \pi$
$\int_0^\infty{e^{-x^2}\,dx} = \frac{1}{2}\sqrt \pi$
$\int_0^\infty{\frac{x}{e^x-1}\,dx} = \frac{\pi^2}{6}$
$\int_0^\infty{\frac{x^3}{e^x-1}\,dx} = \frac{\pi^4}{15}$
$\int_0^\infty\frac{\sin(x)}{x}\,dx=\frac{\pi}{2}$

terça-feira, 19 de novembro de 2013