Exponential function: Integration (formula 01.03.21.0481)

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 e^{d z}

http://functions.wolfram.com/01.03.21.0481.01

Input Form

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