Optimal. Leaf size=22 \[ 5 x \left (e^{2 x^2}-e^{4+x^2}+\log (3)\right ) \]
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Rubi [A]
time = 0.10, antiderivative size = 26, normalized size of antiderivative = 1.18, number of steps
used = 11, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {2258, 2235,
2243} \begin {gather*} 5 e^{2 x^2} x-5 e^{x^2+4} x+5 x \log (3) \end {gather*}
Antiderivative was successfully verified.
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Rule 2235
Rule 2243
Rule 2258
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 x \log (3)+\int e^{4+x^2} \left (-5-10 x^2\right ) \, dx+\int e^{2 x^2} \left (5+20 x^2\right ) \, dx\\ &=5 x \log (3)+\int \left (5 e^{2 x^2}+20 e^{2 x^2} x^2\right ) \, dx+\int \left (-5 e^{4+x^2}-10 e^{4+x^2} x^2\right ) \, dx\\ &=5 x \log (3)+5 \int e^{2 x^2} \, dx-5 \int e^{4+x^2} \, dx-10 \int e^{4+x^2} x^2 \, dx+20 \int e^{2 x^2} x^2 \, dx\\ &=5 e^{2 x^2} x-5 e^{4+x^2} x-\frac {5}{2} e^4 \sqrt {\pi } \text {erfi}(x)+\frac {5}{2} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} x\right )+5 x \log (3)-5 \int e^{2 x^2} \, dx+5 \int e^{4+x^2} \, dx\\ &=5 e^{2 x^2} x-5 e^{4+x^2} x+5 x \log (3)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 25, normalized size = 1.14 \begin {gather*} 5 e^{2 x^2} x-5 e^{4+x^2} x+x \log (243) \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.47, size = 44, normalized size = 2.00
method | result | size |
norman | \(5 x \,{\mathrm e}^{2 x^{2}}+5 x \ln \left (3\right )-5 x \,{\mathrm e}^{4} {\mathrm e}^{x^{2}}\) | \(25\) |
risch | \(5 x \,{\mathrm e}^{2 x^{2}}-5 x \,{\mathrm e}^{x^{2}+4}+5 x \ln \left (3\right )\) | \(25\) |
default | \(-\frac {5 \,{\mathrm e}^{4} \sqrt {\pi }\, \erfi \left (x \right )}{2}-10 \,{\mathrm e}^{4} \left (\frac {{\mathrm e}^{x^{2}} x}{2}-\frac {\sqrt {\pi }\, \erfi \left (x \right )}{4}\right )+5 x \,{\mathrm e}^{2 x^{2}}+5 x \ln \left (3\right )\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 24, normalized size = 1.09 \begin {gather*} 5 \, x e^{\left (2 \, x^{2}\right )} - 5 \, x e^{\left (x^{2} + 4\right )} + 5 \, x \log \left (3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 30, normalized size = 1.36 \begin {gather*} 5 \, {\left (x e^{8} \log \left (3\right ) + x e^{\left (2 \, x^{2} + 8\right )} - x e^{\left (x^{2} + 12\right )}\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 32, normalized size = 1.45 \begin {gather*} 5 x e^{2 x^{2}} - 5 x e^{4} \sqrt {e^{2 x^{2}}} + 5 x \log {\left (3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 24, normalized size = 1.09 \begin {gather*} 5 \, x e^{\left (2 \, x^{2}\right )} - 5 \, x e^{\left (x^{2} + 4\right )} + 5 \, x \log \left (3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 20, normalized size = 0.91 \begin {gather*} 5\,x\,\left (\ln \left (3\right )+{\mathrm {e}}^{2\,x^2}-{\mathrm {e}}^{x^2+4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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