Exponential function: Integration (formula 01.03.21.0468)

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 c^{d z})^beta e^{f z}

http://functions.wolfram.com/01.03.21.0468.01

Input Form

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

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