Optimal. Leaf size=24 \[ (-\log (\log (x)))^{-n} \log ^n(\log (x)) \text{Gamma}(n+1,-\log (\log (x))) \]
[Out]
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Rubi [A] time = 0.0497788, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ (-\log (\log (x)))^{-n} \log ^n(\log (x)) \text{Gamma}(n+1,-\log (\log (x))) \]
Antiderivative was successfully verified.
[In] Int[Log[Log[x]]^n/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\log{\left (\log{\left (x \right )} \right )}^{n}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(ln(x))**n/x,x)
[Out]
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Mathematica [A] time = 0.0177344, size = 24, normalized size = 1. \[ (-\log (\log (x)))^{-n} \log ^n(\log (x)) \text{Gamma}(n+1,-\log (\log (x))) \]
Antiderivative was successfully verified.
[In] Integrate[Log[Log[x]]^n/x,x]
[Out]
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Maple [F] time = 0.038, size = 0, normalized size = 0. \[ \int{\frac{ \left ( \ln \left ( \ln \left ( x \right ) \right ) \right ) ^{n}}{x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(ln(x))^n/x,x)
[Out]
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Maxima [A] time = 1.45075, size = 39, normalized size = 1.62 \[ -\left (-\log \left (\log \left (x\right )\right )\right )^{-n - 1} \log \left (\log \left (x\right )\right )^{n + 1} \Gamma \left (n + 1, -\log \left (\log \left (x\right )\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(log(x))^n/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.276443, size = 19, normalized size = 0.79 \[ \cos \left (\pi n\right ) \Gamma \left (n + 1, -\log \left (\log \left (x\right )\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(log(x))^n/x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\log{\left (\log{\left (x \right )} \right )}^{n}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(ln(x))**n/x,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\log \left (\log \left (x\right )\right )^{n}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(log(x))^n/x,x, algorithm="giac")
[Out]