Hyperbolic Integral

hyperbolic_integral(first_constant, second_constant, precision=4)

Generates the integral of a hyperbolic function

Parameters

• first_constant (int or float) – Coefficient of the reciprocal variable of the original hyperbolic 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 hyperbolic 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

hyperbolic_equation(), hyperbolic_derivatives(), hyperbolic_roots(), hyperbolic_model()

Notes

• Standard form of a hyperbolic function: \(f(x) = a\cdot{\frac{1}{x}} + b\)

• Integral of a hyperbolic function: \(F(x) = a\cdot{\ln|x|} + b\cdot{x}\)

• Basic Properties of Indefinite Integrals

• Basic Integration Forumulas

Examples

Import sinusoidal_hyperbolic function from regressions library

>>> from regressions.analyses.hyperbolics.sinusoidal import sinusoidal_hyperbolic

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

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

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

>>> integral_evaluation = hyperbolic_integral(-2, 3)
>>> print(integral_evaluation['evaluation'](10))
25.3948

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

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