Exponential function: Integration (formula 01.03.21.0779)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Integration

Indefinite integration

Involving functions of the direct function and a power function

Involving rational functions of the direct function and a power function

Involving zⁿ e^{c z}/a+b e^{c z}

http://functions.wolfram.com/01.03.21.0779.01

Input Form

Integrate[(z e^(f z))/(a + b c^(d z)), z] == (1/a) (e^(f z) (-(LerchPhi[-((b c^(d z))/a), 2, (f Log[e])/(d Log[c])]/ (d^2 Log[c]^2)) + (z Hypergeometric2F1[1, (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), -((b c^(d z))/a)])/(f Log[e])))

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