Optimal. Leaf size=26 \[ \frac {3}{-3+2 \left (e^{x^2}-\frac {x}{5}\right ) x^2 \log ^2(3)} \]
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Rubi [A]
time = 0.19, antiderivative size = 29, normalized size of antiderivative = 1.12, number of steps
used = 3, number of rules used = 3, integrand size = 93, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {6820, 12, 6818}
\begin {gather*} -\frac {15}{2 x^3 \log ^2(3)-10 e^{x^2} x^2 \log ^2(3)+15} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {30 x \left (3 x-10 e^{x^2} \left (1+x^2\right )\right ) \log ^2(3)}{\left (15-10 e^{x^2} x^2 \log ^2(3)+2 x^3 \log ^2(3)\right )^2} \, dx\\ &=\left (30 \log ^2(3)\right ) \int \frac {x \left (3 x-10 e^{x^2} \left (1+x^2\right )\right )}{\left (15-10 e^{x^2} x^2 \log ^2(3)+2 x^3 \log ^2(3)\right )^2} \, dx\\ &=-\frac {15}{15-10 e^{x^2} x^2 \log ^2(3)+2 x^3 \log ^2(3)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 38, normalized size = 1.46 \begin {gather*} -\frac {30 \log ^2(3)}{30 \log ^2(3)-20 e^{x^2} x^2 \log ^4(3)+4 x^3 \log ^4(3)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.63, size = 29, normalized size = 1.12
method | result | size |
risch | \(-\frac {15}{2 x^{3} \ln \left (3\right )^{2}-10 \ln \left (3\right )^{2} {\mathrm e}^{x^{2}} x^{2}+15}\) | \(29\) |
norman | \(\frac {2 x^{3} \ln \left (3\right )^{2}-10 \ln \left (3\right )^{2} {\mathrm e}^{x^{2}} x^{2}}{2 x^{3} \ln \left (3\right )^{2}-10 \ln \left (3\right )^{2} {\mathrm e}^{x^{2}} x^{2}+15}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 28, normalized size = 1.08 \begin {gather*} -\frac {15}{2 \, x^{3} \log \left (3\right )^{2} - 10 \, x^{2} e^{\left (x^{2}\right )} \log \left (3\right )^{2} + 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 28, normalized size = 1.08 \begin {gather*} -\frac {15}{2 \, x^{3} \log \left (3\right )^{2} - 10 \, x^{2} e^{\left (x^{2}\right )} \log \left (3\right )^{2} + 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 27, normalized size = 1.04 \begin {gather*} \frac {15}{- 2 x^{3} \log {\left (3 \right )}^{2} + 10 x^{2} e^{x^{2}} \log {\left (3 \right )}^{2} - 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 28, normalized size = 1.08 \begin {gather*} -\frac {15}{2 \, x^{3} \log \left (3\right )^{2} - 10 \, x^{2} e^{\left (x^{2}\right )} \log \left (3\right )^{2} + 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {90\,x^2\,{\ln \left (3\right )}^2-{\mathrm {e}}^{x^2}\,{\ln \left (3\right )}^2\,\left (300\,x^3+300\,x\right )}{60\,x^3\,{\ln \left (3\right )}^2-{\mathrm {e}}^{x^2}\,\left (40\,{\ln \left (3\right )}^4\,x^5+300\,{\ln \left (3\right )}^2\,x^2\right )+4\,x^6\,{\ln \left (3\right )}^4+100\,x^4\,{\mathrm {e}}^{2\,x^2}\,{\ln \left (3\right )}^4+225} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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