Search for a tool
Primitives Functions

Tool to find primitives of functions. Integration of a function is the calculation of all its primitives, the inverse of the derivative.

Results

Primitives Functions -

Tag(s) : Functions, Symbolic Computation

Share
Share
dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Thanks to your feedback and relevant comments, dCode has developped the best Primitives Functions tool, so feel free to write! Thank you !

Primitives Functions

Primitive Function Calculator



Tool to find primitives of functions. Integration of a function is the calculation of all its primitives, the inverse of the derivative.

Answers to Questions

How to calculate a primitive/integral?

The primitive of a function $ f $ defined over an interval $ I $ is a function $ F $ (usually noted in uppercase), defined and differentiable over $ I $, which derivative is $ f $, ie. $ F'(x) = f(x) $.

Example: If $ f(x) = x^2+sin(x) $ then the primitive is $ F(x) = \frac{1}{3}x^3-cos(x) + C $ (with $ C $ a constant).

dCode knows all functions and their primitives. Enter the function and its variable to integrate and dCode do the computation of the primitive function.

Mathematicians use primitive/integration to find the function calculating the area under the curve.

What is the list of common primitives?

FunctionPrimitive
$$ \int \,\rm dx $$$$ x + C $$
$$ \int x^n\,\rm dx $$$$ \frac{x^{n+1}}{n+1} + C \qquad n \ne -1 $$
$$ \int \frac{1}{x}\,\rm dx $$$$ \ln \left| x \right| + C \qquad x \ne 0 $$
$$ \int \frac{1}{x-a} \, \rm dx $$$$ \ln | x-a | + C \qquad x \ne a $$
$$ \int \frac{1}{(x-a)^n} \, \rm dx $$$$-\frac{1}{(n-1)(x-a)^{n-1}} + C \qquad n \ne 1 , x \ne a $$
$$ \int \frac{1}{1+x^2} \, \rm dx $$$$ \operatorname{arctan}(x) + C $$
$$ \int \frac{1}{a^2+x^2} \, \rm dx $$$$ \frac{1}{a}\operatorname{arctan}{ \left( \frac{x}{a} \right) } + C \qquad a \ne 0 $$
$$ \int \frac{1}{1-x^2} \, \rm dx $$$$ \frac{1}{2} \ln { \left| \frac{x+1}{x-1} \right| } + C $$
$$ \int \ln (x)\,\rm dx $$$$ x \ln (x) - x + C $$
$$ \int \log_b (x)\,\rm dx $$$$ x \log_b (x) - x \log_b (e) + C $$
$$ \int e^x\,\rm dx $$$ e^x + C $$
$$ \int a^x\,\rm dx $$$ \frac{a^x}{\ln (a)} + C \qquad a > 0 , a \ne 1 $$
$$ \int {1 \over \sqrt{1-x^2}} \, \rm dx $$$ \operatorname{arcsin} (x) + C $$
$$ \int {-1 \over \sqrt{1-x^2}} \, \rm dx $$$ \operatorname{arccos} (x) + C $$
$$ \int {x \over \sqrt{x^2-1}} \, \rm dx $$$ \sqrt{x^2-1} + C $$
$$ \int \sin(x)\,\rm dx $$$$ -\cos(x)+C $$
$$ \int \cos(x)\,\rm dx $$$$ \sin(x)+C $$
$$ \int \tan(x)\,\rm dx $$$$ -\ln|\cos(x)|+C $$

The primitive calculation of some functions within dCode calculator can involve the functions denoted $ F $ and $ E $ respectively first and second kind of elliptic integrals, or $ Ci $ and $ Si $ respectively Cosine Integral and Sine Integral, or $ Li_2 $ the Spence's function or $ B_x $ the Euler Beta function.

Source code

dCode retains ownership of the source code of the script Primitives Functions online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Primitives Functions script for offline use on PC, iPhone or Android, ask for price quote on contact page !

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developped the best Primitives Functions tool, so feel free to write! Thank you !


Source : https://www.dcode.fr/primitive-integral
© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback