Optimal. Leaf size=22 \[ -3+\frac {2 e^{x^2}}{5}+2 x+x^2 \log ^2(3) \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 3, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {12, 2209} \begin {gather*} \frac {2 e^{x^2}}{5}+x^2 \log ^2(3)+2 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (10+4 e^{x^2} x+10 x \log ^2(3)\right ) \, dx\\ &=2 x+x^2 \log ^2(3)+\frac {4}{5} \int e^{x^2} x \, dx\\ &=\frac {2 e^{x^2}}{5}+2 x+x^2 \log ^2(3)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.95 \begin {gather*} \frac {2 e^{x^2}}{5}+2 x+x^2 \log ^2(3) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 18, normalized size = 0.82 \begin {gather*} x^{2} \log \relax (3)^{2} + 2 \, x + \frac {2}{5} \, e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 18, normalized size = 0.82 \begin {gather*} x^{2} \log \relax (3)^{2} + 2 \, x + \frac {2}{5} \, e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 19, normalized size = 0.86
method | result | size |
default | \(2 x +x^{2} \ln \relax (3)^{2}+\frac {2 \,{\mathrm e}^{x^{2}}}{5}\) | \(19\) |
norman | \(2 x +x^{2} \ln \relax (3)^{2}+\frac {2 \,{\mathrm e}^{x^{2}}}{5}\) | \(19\) |
risch | \(2 x +x^{2} \ln \relax (3)^{2}+\frac {2 \,{\mathrm e}^{x^{2}}}{5}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 18, normalized size = 0.82 \begin {gather*} x^{2} \log \relax (3)^{2} + 2 \, x + \frac {2}{5} \, e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.31, size = 18, normalized size = 0.82 \begin {gather*} 2\,x+\frac {2\,{\mathrm {e}}^{x^2}}{5}+x^2\,{\ln \relax (3)}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 19, normalized size = 0.86 \begin {gather*} x^{2} \log {\relax (3 )}^{2} + 2 x + \frac {2 e^{x^{2}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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