Optimal. Leaf size=29 \[ \log \left (\frac {5}{2}\right ) \left (-2+\frac {1}{2} \left (-3+x+\frac {x}{e^5}+x^2+\frac {x}{\log (\log (x))}\right )\right ) \]
________________________________________________________________________________________
Rubi [F] time = 0.20, 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 {-e^5 \log \left (\frac {5}{2}\right )+e^5 \log \left (\frac {5}{2}\right ) \log (x) \log (\log (x))+\left (1+e^5 (1+2 x)\right ) \log \left (\frac {5}{2}\right ) \log (x) \log ^2(\log (x))}{2 e^5 \log (x) \log ^2(\log (x))} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-e^5 \log \left (\frac {5}{2}\right )+e^5 \log \left (\frac {5}{2}\right ) \log (x) \log (\log (x))+\left (1+e^5 (1+2 x)\right ) \log \left (\frac {5}{2}\right ) \log (x) \log ^2(\log (x))}{\log (x) \log ^2(\log (x))} \, dx}{2 e^5}\\ &=\frac {\int \left (\left (1+e^5+2 e^5 x\right ) \log \left (\frac {5}{2}\right )-\frac {e^5 \log \left (\frac {5}{2}\right )}{\log (x) \log ^2(\log (x))}+\frac {e^5 \log \left (\frac {5}{2}\right )}{\log (\log (x))}\right ) \, dx}{2 e^5}\\ &=\frac {\left (1+e^5+2 e^5 x\right )^2 \log \left (\frac {5}{2}\right )}{8 e^{10}}-\frac {1}{2} \log \left (\frac {5}{2}\right ) \int \frac {1}{\log (x) \log ^2(\log (x))} \, dx+\frac {1}{2} \log \left (\frac {5}{2}\right ) \int \frac {1}{\log (\log (x))} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.09, size = 30, normalized size = 1.03 \begin {gather*} \frac {x \log \left (\frac {5}{2}\right ) \left (1+e^5 (1+x)+\frac {e^5}{\log (\log (x))}\right )}{2 e^5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.67, size = 32, normalized size = 1.10 \begin {gather*} \frac {{\left (x e^{5} \log \left (\frac {5}{2}\right ) + {\left ({\left (x^{2} + x\right )} e^{5} + x\right )} \log \left (\frac {5}{2}\right ) \log \left (\log \relax (x)\right )\right )} e^{\left (-5\right )}}{2 \, \log \left (\log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.77, size = 67, normalized size = 2.31 \begin {gather*} \frac {1}{2} \, {\left (x^{2} e^{5} \log \relax (5) - x^{2} e^{5} \log \relax (2) + x e^{5} \log \relax (5) - x e^{5} \log \relax (2) + x \log \relax (5) - x \log \relax (2) + \frac {x e^{5} \log \relax (5)}{\log \left (\log \relax (x)\right )} - \frac {x e^{5} \log \relax (2)}{\log \left (\log \relax (x)\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.14, size = 55, normalized size = 1.90
method | result | size |
risch | \(-\frac {x^{2} \ln \relax (2)}{2}+\frac {x^{2} \ln \relax (5)}{2}-\frac {x \ln \relax (2)}{2}+\frac {x \ln \relax (5)}{2}-\frac {{\mathrm e}^{-5} x \ln \relax (2)}{2}+\frac {x \ln \relax (5) {\mathrm e}^{-5}}{2}-\frac {x \left (\ln \relax (2)-\ln \relax (5)\right )}{2 \ln \left (\ln \relax (x )\right )}\) | \(55\) |
norman | \(\frac {\left (-\frac {\ln \relax (2)}{2}+\frac {\ln \relax (5)}{2}\right ) x +\left (-\frac {\ln \relax (2)}{2}+\frac {\ln \relax (5)}{2}\right ) x^{2} \ln \left (\ln \relax (x )\right )-\frac {{\mathrm e}^{-5} \left ({\mathrm e}^{5} \ln \relax (2)-{\mathrm e}^{5} \ln \relax (5)+\ln \relax (2)-\ln \relax (5)\right ) x \ln \left (\ln \relax (x )\right )}{2}}{\ln \left (\ln \relax (x )\right )}\) | \(63\) |
default | \(\frac {{\mathrm e}^{-5} \left (\frac {\left (-{\mathrm e}^{5} \ln \relax (2)-\ln \relax (2)\right ) x \ln \left (\ln \relax (x )\right )-x \,{\mathrm e}^{5} \ln \relax (2)-{\mathrm e}^{5} \ln \relax (2) x^{2} \ln \left (\ln \relax (x )\right )}{\ln \left (\ln \relax (x )\right )}+\frac {\left ({\mathrm e}^{5} \ln \relax (5)+\ln \relax (5)\right ) x \ln \left (\ln \relax (x )\right )+x \,{\mathrm e}^{5} \ln \relax (5)+{\mathrm e}^{5} \ln \relax (5) x^{2} \ln \left (\ln \relax (x )\right )}{\ln \left (\ln \relax (x )\right )}\right )}{2}\) | \(87\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.60, size = 39, normalized size = 1.34 \begin {gather*} \frac {1}{2} \, {\left (x^{2} e^{5} \log \left (\frac {5}{2}\right ) + x e^{5} \log \left (\frac {5}{2}\right ) + x \log \left (\frac {5}{2}\right ) + \frac {x {\left (\log \relax (5) - \log \relax (2)\right )} e^{5}}{\log \left (\log \relax (x)\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.96, size = 31, normalized size = 1.07 \begin {gather*} x\,\left (\frac {\ln \left (\frac {5}{2}\right )}{2}+\frac {{\mathrm {e}}^{-5}\,\ln \left (\frac {5}{2}\right )}{2}\right )+\frac {x^2\,\ln \left (\frac {5}{2}\right )}{2}+\frac {x\,\ln \left (\frac {5}{2}\right )}{2\,\ln \left (\ln \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.28, size = 56, normalized size = 1.93 \begin {gather*} x^{2} \left (- \frac {\log {\relax (2 )}}{2} + \frac {\log {\relax (5 )}}{2}\right ) + \frac {x \left (- e^{5} \log {\relax (2 )} - \log {\relax (2 )} + \log {\relax (5 )} + e^{5} \log {\relax (5 )}\right )}{2 e^{5}} + \frac {- x \log {\relax (2 )} + x \log {\relax (5 )}}{2 \log {\left (\log {\relax (x )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________