Optimal. Leaf size=25 \[ x \left (x+x \left (2+e^{-e^4} x-\log (2)+\log ^2(2)\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.24, number of steps used = 2, number of rules used = 1, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {12} \begin {gather*} e^{-e^4} x^3+\frac {1}{2} x^2 \left (6+2 \log ^2(2)-\log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-e^4} \int \left (3 x^2+e^{e^4} \left (6 x-2 x \log (2)+2 x \log ^2(2)\right )\right ) \, dx\\ &=e^{-e^4} x^3+\frac {1}{2} x^2 \left (6+2 \log ^2(2)-\log (4)\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 31, normalized size = 1.24 \begin {gather*} e^{-e^4} x^3+\frac {1}{2} x^2 \left (6+2 \log ^2(2)-\log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.88, size = 35, normalized size = 1.40 \begin {gather*} {\left (x^{3} + {\left (x^{2} \log \relax (2)^{2} - x^{2} \log \relax (2) + 3 \, x^{2}\right )} e^{\left (e^{4}\right )}\right )} e^{\left (-e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 35, normalized size = 1.40 \begin {gather*} {\left (x^{3} + {\left (x^{2} \log \relax (2)^{2} - x^{2} \log \relax (2) + 3 \, x^{2}\right )} e^{\left (e^{4}\right )}\right )} e^{\left (-e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 25, normalized size = 1.00
method | result | size |
norman | \(\left (\ln \relax (2)^{2}-\ln \relax (2)+3\right ) x^{2}+{\mathrm e}^{-{\mathrm e}^{4}} x^{3}\) | \(25\) |
gosper | \(\left (\ln \relax (2)^{2} {\mathrm e}^{{\mathrm e}^{4}}-\ln \relax (2) {\mathrm e}^{{\mathrm e}^{4}}+3 \,{\mathrm e}^{{\mathrm e}^{4}}+x \right ) x^{2} {\mathrm e}^{-{\mathrm e}^{4}}\) | \(32\) |
default | \({\mathrm e}^{-{\mathrm e}^{4}} \left ({\mathrm e}^{{\mathrm e}^{4}} \left (x^{2} \ln \relax (2)^{2}-x^{2} \ln \relax (2)+3 x^{2}\right )+x^{3}\right )\) | \(36\) |
risch | \({\mathrm e}^{-{\mathrm e}^{4}} x^{3}+\ln \relax (2)^{2} {\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{{\mathrm e}^{4}} x^{2}-\ln \relax (2) {\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{{\mathrm e}^{4}} x^{2}+3 \,{\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{{\mathrm e}^{4}} x^{2}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.35, size = 35, normalized size = 1.40 \begin {gather*} {\left (x^{3} + {\left (x^{2} \log \relax (2)^{2} - x^{2} \log \relax (2) + 3 \, x^{2}\right )} e^{\left (e^{4}\right )}\right )} e^{\left (-e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 6.55, size = 24, normalized size = 0.96 \begin {gather*} {\mathrm {e}}^{-{\mathrm {e}}^4}\,x^3+\left ({\ln \relax (2)}^2-\ln \relax (2)+3\right )\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 20, normalized size = 0.80 \begin {gather*} \frac {x^{3}}{e^{e^{4}}} + x^{2} \left (- \log {\relax (2 )} + \log {\relax (2 )}^{2} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________