Exponential function: Integration (formula 01.03.21.0463)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving ((a+b e^{c z})^nu)^beta

http://functions.wolfram.com/01.03.21.0463.01

Input Form

Integrate[((a + b E^(c z))^\[Nu])^\[Beta], z] == (1/(c \[Beta] \[Nu])) ((((a + b E^(c z))^\[Nu])^\[Beta] Hypergeometric2F1[(-\[Beta]) \[Nu], (-\[Beta]) \[Nu], 1 - \[Beta] \[Nu], -(a/(E^(c z) b))])/(1 + a/(E^(c z) b))^(\[Beta] \[Nu]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2002-12-18