Optimal. Leaf size=24 \[ -6-x \left (2 x-x \left (\frac {e^x}{\log (3)}+\log (\log (3))\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.06, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 11, number of rules used = 6, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {6, 12, 1593, 2196, 2176, 2194} \begin {gather*} \frac {e^x x^2}{\log (3)}-x^2 (2-\log (\log (3))) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rule 1593
Rule 2176
Rule 2194
Rule 2196
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x \left (2 x+x^2\right )+x \log (3) (-4+2 \log (\log (3)))}{\log (3)} \, dx\\ &=\frac {\int \left (e^x \left (2 x+x^2\right )+x \log (3) (-4+2 \log (\log (3)))\right ) \, dx}{\log (3)}\\ &=-x^2 (2-\log (\log (3)))+\frac {\int e^x \left (2 x+x^2\right ) \, dx}{\log (3)}\\ &=-x^2 (2-\log (\log (3)))+\frac {\int e^x x (2+x) \, dx}{\log (3)}\\ &=-x^2 (2-\log (\log (3)))+\frac {\int \left (2 e^x x+e^x x^2\right ) \, dx}{\log (3)}\\ &=-x^2 (2-\log (\log (3)))+\frac {\int e^x x^2 \, dx}{\log (3)}+\frac {2 \int e^x x \, dx}{\log (3)}\\ &=\frac {2 e^x x}{\log (3)}+\frac {e^x x^2}{\log (3)}-x^2 (2-\log (\log (3)))-\frac {2 \int e^x \, dx}{\log (3)}-\frac {2 \int e^x x \, dx}{\log (3)}\\ &=-\frac {2 e^x}{\log (3)}+\frac {e^x x^2}{\log (3)}-x^2 (2-\log (\log (3)))+\frac {2 \int e^x \, dx}{\log (3)}\\ &=\frac {e^x x^2}{\log (3)}-x^2 (2-\log (\log (3)))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 20, normalized size = 0.83 \begin {gather*} \frac {x^2 \left (e^x+\log (3) (-2+\log (\log (3)))\right )}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.98, size = 28, normalized size = 1.17 \begin {gather*} \frac {x^{2} \log \relax (3) \log \left (\log \relax (3)\right ) + x^{2} e^{x} - 2 \, x^{2} \log \relax (3)}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.14, size = 28, normalized size = 1.17 \begin {gather*} \frac {x^{2} \log \relax (3) \log \left (\log \relax (3)\right ) + x^{2} e^{x} - 2 \, x^{2} \log \relax (3)}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 21, normalized size = 0.88
method | result | size |
norman | \(\left (\ln \left (\ln \relax (3)\right )-2\right ) x^{2}+\frac {x^{2} {\mathrm e}^{x}}{\ln \relax (3)}\) | \(21\) |
risch | \(x^{2} \ln \left (\ln \relax (3)\right )-2 x^{2}+\frac {x^{2} {\mathrm e}^{x}}{\ln \relax (3)}\) | \(24\) |
default | \(\frac {{\mathrm e}^{x} x^{2}-2 x^{2} \ln \relax (3)+x^{2} \ln \relax (3) \ln \left (\ln \relax (3)\right )}{\ln \relax (3)}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.35, size = 28, normalized size = 1.17 \begin {gather*} \frac {x^{2} \log \relax (3) \log \left (\log \relax (3)\right ) + x^{2} e^{x} - 2 \, x^{2} \log \relax (3)}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 21, normalized size = 0.88 \begin {gather*} \frac {x^2\,\left ({\mathrm {e}}^x-\ln \relax (9)+\ln \relax (3)\,\ln \left (\ln \relax (3)\right )\right )}{\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.16, size = 19, normalized size = 0.79 \begin {gather*} \frac {x^{2} e^{x}}{\log {\relax (3 )}} + x^{2} \left (-2 + \log {\left (\log {\relax (3 )} \right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________