3.170 \(\int \frac{1}{\log (t)} \, dt\)

Optimal. Leaf size=2 \[ \text{LogIntegral}(t) \]

[Out]

LogIntegral[t]

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Rubi [A]  time = 0.00441417, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \text{LogIntegral}(t) \]

Antiderivative was successfully verified.

[In]  Int[Log[t]^(-1),t]

[Out]

LogIntegral[t]

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Rubi in Sympy [A]  time = 0.025008, size = 2, normalized size = 1. \[ \operatorname{li}{\left (t \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/ln(t),t)

[Out]

li(t)

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Mathematica [A]  time = 0.00282961, size = 2, normalized size = 1. \[ \text{LogIntegral}(t) \]

Antiderivative was successfully verified.

[In]  Integrate[Log[t]^(-1),t]

[Out]

LogIntegral[t]

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Maple [B]  time = 0.007, size = 9, normalized size = 4.5 \[ -{\it Ei} \left ( 1,-\ln \left ( t \right ) \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/ln(t),t)

[Out]

-Ei(1,-ln(t))

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Maxima [A]  time = 1.42204, size = 4, normalized size = 2. \[{\rm Ei}\left (\log \left (t\right )\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Ei(log(t))

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Fricas [F]  time = 0., size = 0, normalized size = 0. \[ log_integral\left (t\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

log_integral(t)

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\log{\left (t \right )}}\, dt \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/ln(t),t)

[Out]

Integral(1/log(t), t)

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GIAC/XCAS [A]  time = 0.228751, size = 4, normalized size = 2. \[{\rm Ei}\left ({\rm ln}\left (t\right )\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Ei(ln(t))