3.16 \(\int \log (x) \, dx\)

Optimal. Leaf size=8 \[ x \log (x)-x \]

[Out]

-x + x*Log[x]

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Rubi [A]  time = 0.00288465, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ x \log (x)-x \]

Antiderivative was successfully verified.

[In]  Int[Log[x],x]

[Out]

-x + x*Log[x]

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Rubi in Sympy [A]  time = 0.453226, size = 5, normalized size = 0.62 \[ x \log{\left (x \right )} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(ln(x),x)

[Out]

x*log(x) - x

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Mathematica [A]  time = 0.000831316, size = 8, normalized size = 1. \[ x \log (x)-x \]

Antiderivative was successfully verified.

[In]  Integrate[Log[x],x]

[Out]

-x + x*Log[x]

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Maple [A]  time = 0., size = 9, normalized size = 1.1 \[ -x+x\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(ln(x),x)

[Out]

-x+x*ln(x)

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Maxima [A]  time = 1.34864, size = 11, normalized size = 1.38 \[ x \log \left (x\right ) - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(log(x),x, algorithm="maxima")

[Out]

x*log(x) - x

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Fricas [A]  time = 0.215977, size = 11, normalized size = 1.38 \[ x \log \left (x\right ) - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(log(x),x, algorithm="fricas")

[Out]

x*log(x) - x

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Sympy [A]  time = 0.064165, size = 5, normalized size = 0.62 \[ x \log{\left (x \right )} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(ln(x),x)

[Out]

x*log(x) - x

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GIAC/XCAS [A]  time = 0.200761, size = 11, normalized size = 1.38 \[ x{\rm ln}\left (x\right ) - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(log(x),x, algorithm="giac")

[Out]

x*ln(x) - x