Optimal. Leaf size=23 \[ \frac{2}{3} (\log (x)+1)^{3/2}-2 \sqrt{\log (x)+1} \]
[Out]
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Rubi [A] time = 0.065073, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{2}{3} (\log (x)+1)^{3/2}-2 \sqrt{\log (x)+1} \]
Antiderivative was successfully verified.
[In] Int[Log[x]/(x*Sqrt[1 + Log[x]]),x]
[Out]
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Rubi in Sympy [A] time = 5.06574, size = 24, normalized size = 1.04 \[ - \frac{4 \left (\log{\left (x \right )} + 1\right )^{\frac{3}{2}}}{3} + 2 \sqrt{\log{\left (x \right )} + 1} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(x)/x/(1+ln(x))**(1/2),x)
[Out]
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Mathematica [A] time = 0.00760408, size = 16, normalized size = 0.7 \[ \frac{2}{3} (\log (x)-2) \sqrt{\log (x)+1} \]
Antiderivative was successfully verified.
[In] Integrate[Log[x]/(x*Sqrt[1 + Log[x]]),x]
[Out]
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Maple [A] time = 0.009, size = 18, normalized size = 0.8 \[{\frac{2}{3} \left ( 1+\ln \left ( x \right ) \right ) ^{{\frac{3}{2}}}}-2\,\sqrt{1+\ln \left ( x \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(x)/x/(1+ln(x))^(1/2),x)
[Out]
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Maxima [A] time = 1.50231, size = 23, normalized size = 1. \[ \frac{2}{3} \,{\left (\log \left (x\right ) + 1\right )}^{\frac{3}{2}} - 2 \, \sqrt{\log \left (x\right ) + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x)/(x*sqrt(log(x) + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203332, size = 16, normalized size = 0.7 \[ \frac{2}{3} \, \sqrt{\log \left (x\right ) + 1}{\left (\log \left (x\right ) - 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x)/(x*sqrt(log(x) + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.43454, size = 20, normalized size = 0.87 \[ \frac{2 \left (\log{\left (x \right )} + 1\right )^{\frac{3}{2}}}{3} - 2 \sqrt{\log{\left (x \right )} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(x)/x/(1+ln(x))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.2355, size = 23, normalized size = 1. \[ \frac{2}{3} \,{\left ({\rm ln}\left (x\right ) + 1\right )}^{\frac{3}{2}} - 2 \, \sqrt{{\rm ln}\left (x\right ) + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(log(x)/(x*sqrt(log(x) + 1)),x, algorithm="giac")
[Out]