Optimal. Leaf size=12 \[ \frac{\log ^{n+1}(x)}{n+1} \]
[Out]
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Rubi [A] time = 0.027003, antiderivative size = 12, 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 \[ \frac{\log ^{n+1}(x)}{n+1} \]
Antiderivative was successfully verified.
[In] Int[Log[x]^n/x,x]
[Out]
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Rubi in Sympy [A] time = 1.67372, size = 8, normalized size = 0.67 \[ \frac{\log{\left (x \right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(x)**n/x,x)
[Out]
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Mathematica [A] time = 0.00357997, size = 12, normalized size = 1. \[ \frac{\log ^{n+1}(x)}{n+1} \]
Antiderivative was successfully verified.
[In] Integrate[Log[x]^n/x,x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 1.1 \[{\frac{ \left ( \ln \left ( x \right ) \right ) ^{1+n}}{1+n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(x)^n/x,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x)^n/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218214, size = 16, normalized size = 1.33 \[ \frac{\log \left (x\right )^{n} \log \left (x\right )}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x)^n/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.2244, size = 15, normalized size = 1.25 \[ \begin{cases} \frac{\log{\left (x \right )}^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left (\log{\left (x \right )} \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(x)**n/x,x)
[Out]
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GIAC/XCAS [A] time = 0.198872, size = 16, normalized size = 1.33 \[ \frac{{\rm ln}\left (x\right )^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x)^n/x,x, algorithm="giac")
[Out]