Optimal. Leaf size=33 \[ -e^{3+x}+x-x \left (2 x-\frac {e^{-x^2} x \log (\log (4))}{\log (5)}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.24, antiderivative size = 32, normalized size of antiderivative = 0.97, number of steps
used = 10, number of rules used = 6, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {12, 6874,
2225, 2258, 2240, 2243} \begin {gather*} -2 x^2+\frac {e^{-x^2} x^2 \log (\log (4))}{\log (5)}+x-e^{x+3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2225
Rule 2240
Rule 2243
Rule 2258
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int e^{-x^2} \left (e^{x^2} \left (-e^{3+x} \log (5)+(1-4 x) \log (5)\right )+\left (2 x-2 x^3\right ) \log (\log (4))\right ) \, dx}{\log (5)}\\ &=\frac {\int \left (-\left (\left (-1+e^{3+x}+4 x\right ) \log (5)\right )-2 e^{-x^2} x \left (-1+x^2\right ) \log (\log (4))\right ) \, dx}{\log (5)}\\ &=-\frac {(2 \log (\log (4))) \int e^{-x^2} x \left (-1+x^2\right ) \, dx}{\log (5)}-\int \left (-1+e^{3+x}+4 x\right ) \, dx\\ &=x-2 x^2-\frac {(2 \log (\log (4))) \int \left (-e^{-x^2} x+e^{-x^2} x^3\right ) \, dx}{\log (5)}-\int e^{3+x} \, dx\\ &=-e^{3+x}+x-2 x^2+\frac {(2 \log (\log (4))) \int e^{-x^2} x \, dx}{\log (5)}-\frac {(2 \log (\log (4))) \int e^{-x^2} x^3 \, dx}{\log (5)}\\ &=-e^{3+x}+x-2 x^2-\frac {e^{-x^2} \log (\log (4))}{\log (5)}+\frac {e^{-x^2} x^2 \log (\log (4))}{\log (5)}-\frac {(2 \log (\log (4))) \int e^{-x^2} x \, dx}{\log (5)}\\ &=-e^{3+x}+x-2 x^2+\frac {e^{-x^2} x^2 \log (\log (4))}{\log (5)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.09, size = 32, normalized size = 0.97 \begin {gather*} -e^{3+x}+x-2 x^2+\frac {e^{-x^2} x^2 \log (\log (4))}{\log (5)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.22, size = 51, normalized size = 1.55
method | result | size |
risch | \(-2 x^{2}+x +\frac {\left (\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )\right ) x^{2} {\mathrm e}^{-x^{2}}}{\ln \left (5\right )}-{\mathrm e}^{3+x}\) | \(34\) |
norman | \(\left ({\mathrm e}^{x^{2}} x +\frac {\left (\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )\right ) x^{2}}{\ln \left (5\right )}-2 x^{2} {\mathrm e}^{x^{2}}-{\mathrm e}^{x^{2}} {\mathrm e}^{3+x}\right ) {\mathrm e}^{-x^{2}}\) | \(48\) |
default | \(\frac {-2 x^{2} \ln \left (5\right )-{\mathrm e}^{x} \ln \left (5\right ) {\mathrm e}^{3}+\ln \left (2\right ) {\mathrm e}^{-x^{2}} x^{2}+\ln \left (\ln \left (2\right )\right ) {\mathrm e}^{-x^{2}} x^{2}+x \ln \left (5\right )}{\ln \left (5\right )}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 56, normalized size = 1.70 \begin {gather*} -\frac {2 \, x^{2} \log \left (5\right ) - {\left (x^{2} + 1\right )} e^{\left (-x^{2}\right )} \log \left (2 \, \log \left (2\right )\right ) - x \log \left (5\right ) + e^{\left (x + 3\right )} \log \left (5\right ) + e^{\left (-x^{2}\right )} \log \left (2 \, \log \left (2\right )\right )}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 47, normalized size = 1.42 \begin {gather*} \frac {{\left (x^{2} \log \left (2 \, \log \left (2\right )\right ) - {\left ({\left (2 \, x^{2} - x\right )} \log \left (5\right ) + e^{\left (x + 3\right )} \log \left (5\right )\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-x^{2}\right )}}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.14, size = 34, normalized size = 1.03 \begin {gather*} - 2 x^{2} + x + \frac {\left (x^{2} \log {\left (\log {\left (2 \right )} \right )} + x^{2} \log {\left (2 \right )}\right ) e^{- x^{2}}}{\log {\left (5 \right )}} - e^{x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 48, normalized size = 1.45 \begin {gather*} -\frac {2 \, x^{2} \log \left (5\right ) - {\left (x^{2} \log \left (2\right ) + x^{2} \log \left (\log \left (2\right )\right )\right )} e^{\left (-x^{2}\right )} - x \log \left (5\right ) + e^{\left (x + 3\right )} \log \left (5\right )}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.14, size = 46, normalized size = 1.39 \begin {gather*} x-{\mathrm {e}}^{x+3}-2\,x^2+\frac {x^2\,{\mathrm {e}}^{-x^2}\,\ln \left (2\right )}{\ln \left (5\right )}+\frac {x^2\,{\mathrm {e}}^{-x^2}\,\ln \left (\ln \left (2\right )\right )}{\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________