3.86 \(\int \frac{1}{x} \, dx\)

Optimal. Leaf size=2 \[ \log (x) \]

[Out]

Log[x]

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Rubi [A]  time = 0.00244339, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \log (x) \]

Antiderivative was successfully verified.

[In]  Int[x^(-1),x]

[Out]

Log[x]

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Rubi in Sympy [A]  time = 0.021735, size = 2, normalized size = 1. \[ \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x,x)

[Out]

log(x)

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Mathematica [A]  time = 0.000141432, size = 2, normalized size = 1. \[ \log (x) \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-1),x]

[Out]

Log[x]

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Maple [A]  time = 0., size = 3, normalized size = 1.5 \[ \ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x,x)

[Out]

ln(x)

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Maxima [A]  time = 1.33208, size = 3, normalized size = 1.5 \[ \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

log(x)

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Fricas [A]  time = 0.226681, size = 3, normalized size = 1.5 \[ \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

log(x)

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Sympy [A]  time = 0.025056, size = 2, normalized size = 1. \[ \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x,x)

[Out]

log(x)

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GIAC/XCAS [A]  time = 0.201494, size = 4, normalized size = 2. \[{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

ln(abs(x))