Optimal. Leaf size=12 \[ \frac{\text{PolyLog}(2,1-c x)}{c} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0109987, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {2315} \[ \frac{\text{PolyLog}(2,1-c x)}{c} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2315
Rubi steps
\begin{align*} \int \frac{\log (c x)}{1-c x} \, dx &=\frac{\text{Li}_2(1-c x)}{c}\\ \end{align*}
Mathematica [A] time = 0.0022577, size = 12, normalized size = 1. \[ \frac{\text{PolyLog}(2,1-c x)}{c} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.038, size = 9, normalized size = 0.8 \begin{align*}{\frac{{\it dilog} \left ( cx \right ) }{c}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.21025, size = 65, normalized size = 5.42 \begin{align*} -\frac{\log \left (c x - 1\right ) \log \left (c x\right )}{c} + \frac{\log \left (c x - 1\right ) \log \left (x\right )}{c} - \frac{\log \left (-c x + 1\right ) \log \left (x\right ) +{\rm Li}_2\left (c x\right )}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.977331, size = 26, normalized size = 2.17 \begin{align*} \frac{{\rm Li}_2\left (-c x + 1\right )}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} - \int \frac{\log{\left (c x \right )}}{c x - 1}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int -\frac{\log \left (c x\right )}{c x - 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]