Exponential function: Integration (formula 01.03.21.0798)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Integration

Indefinite integration

Involving functions of the direct function and a power function

Involving algebraic functions of the direct function and a power function

Involving zⁿ e^{f z}(a+b c^{d z})^beta

http://functions.wolfram.com/01.03.21.0798.01

Input Form

Integrate[z^4 e^(f z) (a + b c^(d z))^\[Beta], z] == (1/(f^5 Log[e]^5)) (((a + b c^(d z))^\[Beta] e^(f z) (24 HypergeometricPFQ[{-\[Beta], (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c])}, {1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c])}, -((b c^(d z))/a)] + f z Log[e] (-24 HypergeometricPFQ[{-\[Beta], (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c])}, {1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c])}, -((b c^(d z))/a)] + f z Log[e] (12 HypergeometricPFQ[{-\[Beta], (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c])}, {1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c])}, -((b c^(d z))/a)] + f z Log[e] (-4 HypergeometricPFQ[{-\[Beta], (f Log[e])/(d Log[c]), (f Log[e])/(d Log[c])}, {1 + (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c])}, -((b c^(d z))/a)] + f z Hypergeometric2F1[-\[Beta], (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), -((b c^(d z))/a)] Log[e])))))/ (1 + (b c^(d z))/a)^\[Beta])

Standard Form

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MathML Form

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

2002-12-18