Optimal. Leaf size=3 \[ \tan ^{-1}(\log (x)) \]
[Out]
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Rubi [A] time = 0.0316255, antiderivative size = 3, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \tan ^{-1}(\log (x)) \]
Antiderivative was successfully verified.
[In] Int[1/(x*(1 + Log[x]^2)),x]
[Out]
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Rubi in Sympy [A] time = 3.31803, size = 3, normalized size = 1. \[ \operatorname{atan}{\left (\log{\left (x \right )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(1+ln(x)**2),x)
[Out]
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Mathematica [A] time = 0.00580001, size = 3, normalized size = 1. \[ \tan ^{-1}(\log (x)) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(1 + Log[x]^2)),x]
[Out]
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Maple [A] time = 0.001, size = 4, normalized size = 1.3 \[ \arctan \left ( \ln \left ( x \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(1+ln(x)^2),x)
[Out]
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Maxima [A] time = 1.52938, size = 4, normalized size = 1.33 \[ \arctan \left (\log \left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((log(x)^2 + 1)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244666, size = 4, normalized size = 1.33 \[ \arctan \left (\log \left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((log(x)^2 + 1)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.139617, size = 15, normalized size = 5. \[ \operatorname{RootSum}{\left (4 z^{2} + 1, \left ( i \mapsto i \log{\left (2 i + \log{\left (x \right )} \right )} \right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(1+ln(x)**2),x)
[Out]
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GIAC/XCAS [A] time = 0.200576, size = 4, normalized size = 1.33 \[ \arctan \left ({\rm ln}\left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((log(x)^2 + 1)*x),x, algorithm="giac")
[Out]