Optimal. Leaf size=10 \[ -\frac {t}{\log (t)}+\text {li}(t) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2334, 2335}
\begin {gather*} \text {LogIntegral}(t)-\frac {t}{\log (t)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2334
Rule 2335
Rubi steps
\begin {align*} \int \frac {1}{\log ^2(t)} \, dt &=-\frac {t}{\log (t)}+\int \frac {1}{\log (t)} \, dt\\ &=-\frac {t}{\log (t)}+\text {li}(t)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} -\frac {t}{\log (t)}+\text {li}(t) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 17, normalized size = 1.70
method | result | size |
default | \(-\frac {t}{\ln \left (t \right )}-\expIntegral \left (1, -\ln \left (t \right )\right )\) | \(17\) |
risch | \(-\frac {t}{\ln \left (t \right )}-\expIntegral \left (1, -\ln \left (t \right )\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.01, size = 6, normalized size = 0.60 \begin {gather*} \Gamma \left (-1, -\log \left (t\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.65, size = 14, normalized size = 1.40 \begin {gather*} \frac {\log \left (t\right ) \operatorname {log\_integral}\left (t\right ) - t}{\log \left (t\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.23, size = 7, normalized size = 0.70 \begin {gather*} - \frac {t}{\log {\left (t \right )}} + \operatorname {li}{\left (t \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.51, size = 11, normalized size = 1.10 \begin {gather*} -\frac {t}{\log \left (t\right )} + {\rm Ei}\left (\log \left (t\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 10, normalized size = 1.00 \begin {gather*} \mathrm {logint}\left (t\right )-\frac {t}{\ln \left (t\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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