Exponential Integral

exponential_integral(first_constant, second_constant, precision=4)

Generates the integral of an exponential function

Parameters

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

• second_constant (int or float) – Base rate of variable of the original exponential function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001); if one, it will be converted to a small, near-one decimal value (e.g., 1.0001)

• 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

See also

exponential_equation(), exponential_derivatives(), exponential_roots(), exponential_model()

Notes

• Standard form of an exponential function: \(f(x) = a\cdot{b^x}\)

• Integral of an exponential function: \(F(x) = \frac{a}{\ln{b}}\cdot{b^x}\)

• Basic Properties of Indefinite Integrals

• Basic Integration Forumulas

Examples

Import exponential_integral function from regressions library

>>> from regressions.analyses.integrals.exponential import exponential_integral

Generate the integral of an exponential function with coefficients 2 and 3, then display its coefficients

>>> integral_constants = exponential_integral(2, 3)
>>> print(integral_constants['constants'])
[1.8205, 3.0]

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

>>> integral_evaluation = exponential_integral(-2, 3)
>>> print(integral_evaluation['evaluation'](10))
-107498.7045

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

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