Logarithmic Integral

logarithmic_integral(first_constant, second_constant, precision=4)

Generates the integral of a logarithmic function

Parameters

• first_constant (int or float) – Coefficient of the logarithmic term of the original logarithmic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

• second_constant (int or float) – Coefficient of the constant term of the original logarithmic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

• precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the resultant roots

Raises

• TypeError – First two arguments must be integers or floats

• ValueError – Last argument must be a positive integer

Returns

• integral[‘constants’] (list of float) – Coefficients of the resultant integral

• integral[‘evaluation’] (func) – Function for evaluating the resultant integral at any float or integer argument; if zero inputted as argument, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

See also

logarithmic_equation(), logarithmic_derivatives(), logarithmic_roots(), logarithmic_model()

Notes

• Standard form of a logarithmic function: \(f(x) = a\cdot{\ln{x}} + b\)

• Integral of a logarithmic function: \(F(x) = a\cdot{x}\cdot(\ln{x} - 1) + b\cdot{x}\)

• Basic Properties of Indefinite Integrals

• Basic Integration Forumulas

• Integration by Parts

Examples

Import logarithmic_integral function from regressions library

>>> from regressions.analyses.integrals.logarithmic import logarithmic_integral

Generate the integral of a logarithmic function with coefficients 2 and 3, then display its coefficients

>>> integral_constants = logarithmic_integral(2, 3)
>>> print(integral_constants['constants'])
[2.0, 3.0]

Generate the integral of a logarithmic function with coefficients -2 and 3, then evaluate its integral at 10

>>> integral_evaluation = logarithmic_integral(-2, 3)
>>> print(integral_evaluation['evaluation'](10))
3.9483

Generate the integral of a logarithmic function with all inputs set to 0, then display its coefficients

>>> integral_zeroes = logarithmic_integral(0, 0)
>>> print(integral_zeroes['constants'])
[0.0001, 0.0001]