3.259 \(\int \frac{1}{x \sqrt{\log (x)}} \, dx\)

Optimal. Leaf size=8 \[ 2 \sqrt{\log (x)} \]

[Out]

2*Sqrt[Log[x]]

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Rubi [A]  time = 0.0206341, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ 2 \sqrt{\log (x)} \]

Antiderivative was successfully verified.

[In]  Int[1/(x*Sqrt[Log[x]]),x]

[Out]

2*Sqrt[Log[x]]

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Rubi in Sympy [A]  time = 1.49633, size = 7, normalized size = 0.88 \[ 2 \sqrt{\log{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x/ln(x)**(1/2),x)

[Out]

2*sqrt(log(x))

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Mathematica [A]  time = 0.00179286, size = 8, normalized size = 1. \[ 2 \sqrt{\log (x)} \]

Antiderivative was successfully verified.

[In]  Integrate[1/(x*Sqrt[Log[x]]),x]

[Out]

2*Sqrt[Log[x]]

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Maple [A]  time = 0.006, size = 7, normalized size = 0.9 \[ 2\,\sqrt{\ln \left ( x \right ) } \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x/ln(x)^(1/2),x)

[Out]

2*ln(x)^(1/2)

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Maxima [A]  time = 1.36554, size = 8, normalized size = 1. \[ 2 \, \sqrt{\log \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(x*sqrt(log(x))),x, algorithm="maxima")

[Out]

2*sqrt(log(x))

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Fricas [A]  time = 0.197919, size = 8, normalized size = 1. \[ 2 \, \sqrt{\log \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(x*sqrt(log(x))),x, algorithm="fricas")

[Out]

2*sqrt(log(x))

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Sympy [A]  time = 0.546356, size = 7, normalized size = 0.88 \[ 2 \sqrt{\log{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x/ln(x)**(1/2),x)

[Out]

2*sqrt(log(x))

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GIAC/XCAS [A]  time = 0.215078, size = 8, normalized size = 1. \[ 2 \, \sqrt{{\rm ln}\left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(x*sqrt(log(x))),x, algorithm="giac")

[Out]

2*sqrt(ln(x))