Optimal. Leaf size=4 \[ \operatorname {LogIntegral}(x+1) \]
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Rubi [A] time = 0.00, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2389, 2298} \[ \text {LogIntegral}(x+1) \]
Antiderivative was successfully verified.
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Rule 2298
Rule 2389
Rubi steps
\begin {align*} \int \frac {1}{\log (1+x)} \, dx &=\operatorname {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,1+x\right )\\ &=\text {li}(1+x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 5, normalized size = 1.25 \[ \operatorname {ExpIntegralEi}(\log (x+1)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 4, normalized size = 1.00 \[ \operatorname {log\_integral}\left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.10, size = 5, normalized size = 1.25 \[ {\rm Ei}\left (\log \left (x + 1\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 11, normalized size = 2.75 \[ -\Ei \left (1, -\ln \left (x +1\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 5, normalized size = 1.25 \[ {\rm Ei}\left (\log \left (x + 1\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 4, normalized size = 1.00 \[ \mathrm {logint}\left (x+1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.49, size = 3, normalized size = 0.75 \[ \operatorname {li}{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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