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Primitives Functions

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

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Primitives Functions -

Tag(s) : Mathematics

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# Primitives Functions

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## Primitive Function Calculator

Also on dCode: Definite IntegralDerivative

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

### How to calculate a primitive/integral?

Enter the function and its variable to integrate and dCode do the computation of the primitive function.

Mathematicians talks about finding the function calculating the area under the curve.

dCode knows all functions and their primitives.

### What is the list of common primitives?

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