Optimal. Leaf size=15 \[ \frac{\text{li}(c (d+e x))}{c e} \]
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Rubi [A] time = 0.0092104, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {2389, 2298} \[ \frac{\text{li}(c (d+e x))}{c e} \]
Antiderivative was successfully verified.
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Rule 2389
Rule 2298
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*}
Mathematica [A] time = 0.0076994, size = 15, normalized size = 1. \[ \frac{\text{li}(c (d+e x))}{c e} \]
Antiderivative was successfully verified.
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Maple [F] time = 180., size = 0, normalized size = 0. \begin{align*} \text{hanged} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11473, size = 23, normalized size = 1.53 \begin{align*} \frac{{\rm Ei}\left (\log \left (c e x + c d\right )\right )}{c e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.0023, size = 45, normalized size = 3. \begin{align*} \frac{\logintegral \left (c e x + c d\right )}{c e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.765209, size = 12, normalized size = 0.8 \begin{align*} \frac{\operatorname{li}{\left (c d + c e x \right )}}{c e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27484, size = 22, normalized size = 1.47 \begin{align*} \frac{{\rm Ei}\left (\log \left ({\left (x e + d\right )} c\right )\right ) e^{\left (-1\right )}}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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