Optimal. Leaf size=32 \[ \log \left (1-\frac {\log \left (\frac {\left (5+\frac {e^2}{5}\right ) x}{3 x-e^x x}\right )}{x}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.97, antiderivative size = 24, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 3, integrand size = 78, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6741, 6712, 31} \begin {gather*} \log \left (1-\frac {\log \left (\frac {25+e^2}{15-5 e^x}\right )}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 6712
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^x x+\left (3-e^x\right ) \log \left (\frac {-25-e^2}{-15+5 e^x}\right )}{\left (3-e^x\right ) x \left (x-\log \left (\frac {25+e^2}{15-5 e^x}\right )\right )} \, dx\\ &=-\operatorname {Subst}\left (\int \frac {1}{1-x} \, dx,x,\frac {\log \left (\frac {25+e^2}{15-5 e^x}\right )}{x}\right )\\ &=\log \left (1-\frac {\log \left (\frac {25+e^2}{15-5 e^x}\right )}{x}\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.17, size = 26, normalized size = 0.81 \begin {gather*} -\log (x)+\log \left (x-\log \left (\frac {25+e^2}{15-5 e^x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.55, size = 23, normalized size = 0.72 \begin {gather*} -\log \relax (x) + \log \left (-x + \log \left (-\frac {e^{2} + 25}{5 \, {\left (e^{x} - 3\right )}}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 23, normalized size = 0.72 \begin {gather*} -\log \relax (x) + \log \left (-x + \log \left (-\frac {e^{2} + 25}{5 \, {\left (e^{x} - 3\right )}}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.18, size = 27, normalized size = 0.84
method | result | size |
default | \(-\ln \relax (x )+\ln \left (x -\ln \left (\frac {-{\mathrm e}^{2}-25}{5 \,{\mathrm e}^{x}-15}\right )\right )\) | \(27\) |
norman | \(-\ln \relax (x )+\ln \left (x -\ln \left (\frac {-{\mathrm e}^{2}-25}{5 \,{\mathrm e}^{x}-15}\right )\right )\) | \(27\) |
risch | \(-\ln \relax (x )+\ln \left (\ln \left ({\mathrm e}^{x}-3\right )+\frac {i \left (2 \pi \mathrm {csgn}\left (\frac {i}{{\mathrm e}^{x}-3}\right )^{2}-2 \pi \mathrm {csgn}\left (\frac {i}{{\mathrm e}^{x}-3}\right )^{3}-2 i \ln \relax (5)+2 i \ln \left (-{\mathrm e}^{2}-25\right )-2 i x \right )}{2}\right )\) | \(66\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 24, normalized size = 0.75 \begin {gather*} \log \left (x + \log \relax (5) - \log \left (e^{2} + 25\right ) + \log \left (-e^{x} + 3\right )\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.60, size = 28, normalized size = 0.88 \begin {gather*} \ln \left (x-\ln \left (-\frac {1}{{\mathrm {e}}^x-3}\right )-\ln \left (\frac {{\mathrm {e}}^2}{5}+5\right )\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.24, size = 20, normalized size = 0.62 \begin {gather*} - \log {\relax (x )} + \log {\left (- x + \log {\left (\frac {-25 - e^{2}}{5 e^{x} - 15} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________