Optimal. Leaf size=30 \[ e^4+\frac {3}{\log \left (\log \left (10+e^x+\frac {2}{x \left (\frac {3}{x}+\log (5)\right )}\right )\right )} \]
________________________________________________________________________________________
Rubi [F] time = 7.77, 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*} \int \frac {6 \log (5)+e^x \left (-27-18 x \log (5)-3 x^2 \log ^2(5)\right )}{\left (96+62 x \log (5)+10 x^2 \log ^2(5)+e^x \left (9+6 x \log (5)+x^2 \log ^2(5)\right )\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (2 \log (5)-e^x (3+x \log (5))^2\right )}{(3+x \log (5)) \left (32+10 x \log (5)+e^x (3+x \log (5))\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx\\ &=3 \int \frac {2 \log (5)-e^x (3+x \log (5))^2}{(3+x \log (5)) \left (32+10 x \log (5)+e^x (3+x \log (5))\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx\\ &=3 \int \left (-\frac {1}{\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )}+\frac {2 \left (48+\log (5)+31 x \log (5)+5 x^2 \log ^2(5)\right )}{(3+x \log (5)) \left (32+3 e^x+10 x \log (5)+e^x x \log (5)\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )}\right ) \, dx\\ &=-\left (3 \int \frac {1}{\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx\right )+6 \int \frac {48+\log (5)+31 x \log (5)+5 x^2 \log ^2(5)}{(3+x \log (5)) \left (32+3 e^x+10 x \log (5)+e^x x \log (5)\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx\\ &=-\left (3 \int \frac {1}{\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx\right )+6 \int \left (\frac {16}{\left (32+3 e^x+10 x \log (5)+e^x x \log (5)\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )}+\frac {5 x \log (5)}{\left (32+3 e^x+10 x \log (5)+e^x x \log (5)\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )}+\frac {\log (5)}{(3+x \log (5)) \left (32+3 e^x+10 x \log (5)+e^x x \log (5)\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )}\right ) \, dx\\ &=-\left (3 \int \frac {1}{\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx\right )+96 \int \frac {1}{\left (32+3 e^x+10 x \log (5)+e^x x \log (5)\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx+(6 \log (5)) \int \frac {1}{(3+x \log (5)) \left (32+3 e^x+10 x \log (5)+e^x x \log (5)\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx+(30 \log (5)) \int \frac {x}{\left (32+3 e^x+10 x \log (5)+e^x x \log (5)\right ) \log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right ) \log ^2\left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.07, size = 32, normalized size = 1.07 \begin {gather*} \frac {3}{\log \left (\log \left (\frac {32+10 x \log (5)+e^x (3+x \log (5))}{3+x \log (5)}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.69, size = 31, normalized size = 1.03 \begin {gather*} \frac {3}{\log \left (\log \left (\frac {{\left (x \log \relax (5) + 3\right )} e^{x} + 10 \, x \log \relax (5) + 32}{x \log \relax (5) + 3}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.58, size = 33, normalized size = 1.10 \begin {gather*} \frac {3}{\log \left (\log \left (x e^{x} \log \relax (5) + 10 \, x \log \relax (5) + 3 \, e^{x} + 32\right ) - \log \left (x \log \relax (5) + 3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.22, size = 149, normalized size = 4.97
method | result | size |
risch | \(\frac {3}{\ln \left (-\ln \left (x \ln \relax (5)+3\right )+\ln \left (\ln \relax (5) \left ({\mathrm e}^{x}+10\right ) x +3 \,{\mathrm e}^{x}+32\right )-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \left (\ln \relax (5) \left ({\mathrm e}^{x}+10\right ) x +3 \,{\mathrm e}^{x}+32\right )}{x \ln \relax (5)+3}\right ) \left (-\mathrm {csgn}\left (\frac {i \left (\ln \relax (5) \left ({\mathrm e}^{x}+10\right ) x +3 \,{\mathrm e}^{x}+32\right )}{x \ln \relax (5)+3}\right )+\mathrm {csgn}\left (\frac {i}{x \ln \relax (5)+3}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \left (\ln \relax (5) \left ({\mathrm e}^{x}+10\right ) x +3 \,{\mathrm e}^{x}+32\right )}{x \ln \relax (5)+3}\right )+\mathrm {csgn}\left (i \left (\ln \relax (5) \left ({\mathrm e}^{x}+10\right ) x +3 \,{\mathrm e}^{x}+32\right )\right )\right )}{2}\right )}\) | \(149\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.79, size = 32, normalized size = 1.07 \begin {gather*} \frac {3}{\log \left (\log \left ({\left (x \log \relax (5) + 3\right )} e^{x} + 10 \, x \log \relax (5) + 32\right ) - \log \left (x \log \relax (5) + 3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 8.80, size = 31, normalized size = 1.03 \begin {gather*} \frac {3}{\ln \left (\ln \left (\frac {10\,x\,\ln \relax (5)+{\mathrm {e}}^x\,\left (x\,\ln \relax (5)+3\right )+32}{x\,\ln \relax (5)+3}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 3.90, size = 29, normalized size = 0.97 \begin {gather*} \frac {3}{\log {\left (\log {\left (\frac {10 x \log {\relax (5 )} + \left (x \log {\relax (5 )} + 3\right ) e^{x} + 32}{x \log {\relax (5 )} + 3} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________