Optimal. Leaf size=28 \[ \log \left (e^x \left (-e^{2 x}+x+\log \left (\frac {x (1+x)}{e^x+\log (x)}\right )\right )\right ) \]
________________________________________________________________________________________
Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [A] time = 0.28, size = 28, normalized size = 1.00 \begin {gather*} x+\log \left (e^{2 x}-x-\log \left (\frac {x (1+x)}{e^x+\log (x)}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 25, normalized size = 0.89 \begin {gather*} x + \log \left (x - e^{\left (2 \, x\right )} + \log \left (\frac {x^{2} + x}{e^{x} + \log \relax (x)}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.33, size = 25, normalized size = 0.89 \begin {gather*} x + \log \left (x - e^{\left (2 \, x\right )} + \log \left (x + 1\right ) + \log \relax (x) - \log \left (e^{x} + \log \relax (x)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.19, size = 260, normalized size = 9.29
method | result | size |
risch | \(x +\ln \left (\ln \left (\ln \relax (x )+{\mathrm e}^{x}\right )-\frac {i \left (\pi \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )+{\mathrm e}^{x}}\right ) \mathrm {csgn}\left (\frac {i \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )+{\mathrm e}^{x}}\right ) \mathrm {csgn}\left (\frac {i \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right ) \mathrm {csgn}\left (i \left (x +1\right )\right )-\pi \mathrm {csgn}\left (\frac {i \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right )^{3}+\pi \mathrm {csgn}\left (\frac {i \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right )^{2} \mathrm {csgn}\left (i \left (x +1\right )\right )+\pi \,\mathrm {csgn}\left (\frac {i \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right ) \mathrm {csgn}\left (\frac {i x \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right ) \mathrm {csgn}\left (\frac {i x \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right ) \mathrm {csgn}\left (i x \right )-\pi \mathrm {csgn}\left (\frac {i x \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right )^{3}+\pi \mathrm {csgn}\left (\frac {i x \left (x +1\right )}{\ln \relax (x )+{\mathrm e}^{x}}\right )^{2} \mathrm {csgn}\left (i x \right )+2 i {\mathrm e}^{2 x}-2 i x -2 i \ln \relax (x )-2 i \ln \left (x +1\right )\right )}{2}\right )\) | \(260\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.54, size = 27, normalized size = 0.96 \begin {gather*} x + \log \left (-x + e^{\left (2 \, x\right )} - \log \left (x + 1\right ) - \log \relax (x) + \log \left (e^{x} + \log \relax (x)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.62, size = 24, normalized size = 0.86 \begin {gather*} x+\ln \left (x-{\mathrm {e}}^{2\,x}+\ln \left (\frac {x\,\left (x+1\right )}{{\mathrm {e}}^x+\ln \relax (x)}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.98, size = 22, normalized size = 0.79 \begin {gather*} x + \log {\left (x - e^{2 x} + \log {\left (\frac {x^{2} + x}{e^{x} + \log {\relax (x )}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________