Optimal. Leaf size=15 \[ \frac {\text {li}(c (d+e x))}{c e} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2389, 2298} \[ \frac {\text {li}(c (d+e x))}{c e} \]
Antiderivative was successfully verified.
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Rule 2298
Rule 2389
Rubi steps
\begin {align*} \int \frac {1}{\log (c (d+e x))} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {1}{\log (c x)} \, dx,x,d+e x\right )}{e}\\ &=\frac {\text {li}(c (d+e x))}{c e}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 1.00 \[ \frac {\text {li}(c (d+e x))}{c e} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 16, normalized size = 1.07 \[ \frac {\operatorname {log\_integral}\left (c e x + c d\right )}{c e} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 16, normalized size = 1.07 \[ \frac {{\rm Ei}\left (\log \left ({\left (x e + d\right )} c\right )\right ) e^{\left (-1\right )}}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F(-1)] time = 180.00, size = 0, normalized size = 0.00 \[ \text {hanged} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.09, size = 17, normalized size = 1.13 \[ \frac {{\rm Ei}\left (\log \left (c e x + c d\right )\right )}{c e} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 15, normalized size = 1.00 \[ \frac {\mathrm {logint}\left (c\,\left (d+e\,x\right )\right )}{c\,e} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.75, size = 12, normalized size = 0.80 \[ \frac {\operatorname {li}{\left (c d + c e x \right )}}{c e} \]
Verification of antiderivative is not currently implemented for this CAS.
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