Optimal. Leaf size=22 \[ (-\log (t))^n \log ^{-n}(t) (-\text{Gamma}(-n,-\log (t))) \]
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Rubi [A] time = 0.0290269, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ (-\log (t))^n \log ^{-n}(t) (-\text{Gamma}(-n,-\log (t))) \]
Antiderivative was successfully verified.
[In] Int[Log[t]^(-1 - n),t]
[Out]
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Rubi in Sympy [A] time = 0.584314, size = 24, normalized size = 1.09 \[ \left (- \log{\left (t \right )}\right )^{n + 1} \Gamma{\left (- n,- \log{\left (t \right )} \right )} \log{\left (t \right )}^{- n - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(t)**(-1-n),t)
[Out]
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Mathematica [A] time = 0.0331394, size = 22, normalized size = 1. \[ (-\log (t))^n \log ^{-n}(t) (-\text{Gamma}(-n,-\log (t))) \]
Antiderivative was successfully verified.
[In] Integrate[Log[t]^(-1 - n),t]
[Out]
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Maple [F] time = 0.135, size = 0, normalized size = 0. \[ \int \left ( \ln \left ( t \right ) \right ) ^{-1-n}\, dt \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(t)^(-1-n),t)
[Out]
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Maxima [A] time = 1.50065, size = 30, normalized size = 1.36 \[ -\left (-\log \left (t\right )\right )^{n} \log \left (t\right )^{-n} \Gamma \left (-n, -\log \left (t\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(t)^(-n - 1),t, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226325, size = 20, normalized size = 0.91 \[ \cos \left (\pi + \pi n\right ) \Gamma \left (-n, -\log \left (t\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(t)^(-n - 1),t, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \log{\left (t \right )}^{- n - 1}\, dt \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(t)**(-1-n),t)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \log \left (t\right )^{-n - 1}\,{d t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(t)^(-n - 1),t, algorithm="giac")
[Out]