Optimal. Leaf size=26 \[ x \left (-e^{2 x^2}+\frac {1}{2} \left (-3-3 \left (3+e^{18}+x\right )\right )\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 28, normalized size of antiderivative = 1.08, number of steps used = 7, number of rules used = 4, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.138, Rules used = {12, 2226, 2204, 2212} \begin {gather*} -\frac {3 x^2}{2}-e^{2 x^2} x-\frac {3}{2} \left (4+e^{18}\right ) x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2204
Rule 2212
Rule 2226
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (-12-3 e^{18}-6 x+e^{2 x^2} \left (-2-8 x^2\right )\right ) \, dx\\ &=-\frac {3}{2} \left (4+e^{18}\right ) x-\frac {3 x^2}{2}+\frac {1}{2} \int e^{2 x^2} \left (-2-8 x^2\right ) \, dx\\ &=-\frac {3}{2} \left (4+e^{18}\right ) x-\frac {3 x^2}{2}+\frac {1}{2} \int \left (-2 e^{2 x^2}-8 e^{2 x^2} x^2\right ) \, dx\\ &=-\frac {3}{2} \left (4+e^{18}\right ) x-\frac {3 x^2}{2}-4 \int e^{2 x^2} x^2 \, dx-\int e^{2 x^2} \, dx\\ &=-e^{2 x^2} x-\frac {3}{2} \left (4+e^{18}\right ) x-\frac {3 x^2}{2}-\frac {1}{2} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} x\right )+\int e^{2 x^2} \, dx\\ &=-e^{2 x^2} x-\frac {3}{2} \left (4+e^{18}\right ) x-\frac {3 x^2}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 29, normalized size = 1.12 \begin {gather*} -6 x-\frac {3 e^{18} x}{2}-e^{2 x^2} x-\frac {3 x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 23, normalized size = 0.88 \begin {gather*} -\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{18} - x e^{\left (2 \, x^{2}\right )} - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 23, normalized size = 0.88 \begin {gather*} -\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{18} - x e^{\left (2 \, x^{2}\right )} - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 24, normalized size = 0.92
method | result | size |
default | \(-6 x -\frac {3 x^{2}}{2}-x \,{\mathrm e}^{2 x^{2}}-\frac {3 \,{\mathrm e}^{18} x}{2}\) | \(24\) |
norman | \(\left (-\frac {3 \,{\mathrm e}^{18}}{2}-6\right ) x -\frac {3 x^{2}}{2}-x \,{\mathrm e}^{2 x^{2}}\) | \(24\) |
risch | \(-6 x -\frac {3 x^{2}}{2}-x \,{\mathrm e}^{2 x^{2}}-\frac {3 \,{\mathrm e}^{18} x}{2}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 23, normalized size = 0.88 \begin {gather*} -\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{18} - x e^{\left (2 \, x^{2}\right )} - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.48, size = 20, normalized size = 0.77 \begin {gather*} -\frac {x\,\left (3\,x+3\,{\mathrm {e}}^{18}+2\,{\mathrm {e}}^{2\,x^2}+12\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 26, normalized size = 1.00 \begin {gather*} - \frac {3 x^{2}}{2} - x e^{2 x^{2}} + x \left (- \frac {3 e^{18}}{2} - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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