Basic integrals

\int x^n\,dx=\tfrac{x^{n+1}}{n+1}+C,\ \int\tfrac1x\,dx=\ln|x|+C

Result unit: — (funkcja + C)

What it describes

Basic formulas for indefinite integrals (

C

— the constant of integration).

x

variable

n

exponent

C

constant of integration

Integration is the inverse of differentiation — you add 1 to the exponent and divide. Always include the constant of integration

C

(the derivative of a constant is 0).

Computing indefinite integrals, areas, and antiderivatives.

Compute

\int x^2\,dx

Substitution

n=2

Result

\dfrac{x^3}{3}+C

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