Optimal. Leaf size=12 \[ e^{3 x (1+x)} x^2 \]
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Rubi [B] time = 0.04, antiderivative size = 27, normalized size of antiderivative = 2.25, number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {1594, 2288} \begin {gather*} \frac {e^{3 x^2+3 x} x \left (2 x^2+x\right )}{2 x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 1594
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{3 x+3 x^2} x \left (2+3 x+6 x^2\right ) \, dx\\ &=\frac {e^{3 x+3 x^2} x \left (x+2 x^2\right )}{1+2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} e^{3 x (1+x)} x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 14, normalized size = 1.17 \begin {gather*} x^{2} e^{\left (3 \, x^{2} + 3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 24, normalized size = 2.00 \begin {gather*} \frac {1}{4} \, {\left ({\left (2 \, x + 1\right )}^{2} - 4 \, x - 1\right )} e^{\left (3 \, x^{2} + 3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 12, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{3 \left (x +1\right ) x} x^{2}\) | \(12\) |
gosper | \({\mathrm e}^{3 x^{2}+3 x} x^{2}\) | \(15\) |
default | \({\mathrm e}^{3 x^{2}+3 x} x^{2}\) | \(15\) |
norman | \({\mathrm e}^{3 x^{2}+3 x} x^{2}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.51, size = 268, normalized size = 22.33 \begin {gather*} \frac {1}{72} \, \sqrt {3} {\left (\frac {36 \, {\left (2 \, x + 1\right )}^{3} \Gamma \left (\frac {3}{2}, -\frac {3}{4} \, {\left (2 \, x + 1\right )}^{2}\right )}{\left (-{\left (2 \, x + 1\right )}^{2}\right )^{\frac {3}{2}}} - \frac {9 \, \sqrt {\pi } {\left (2 \, x + 1\right )} {\left (\operatorname {erf}\left (\frac {1}{2} \, \sqrt {3} \sqrt {-{\left (2 \, x + 1\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (2 \, x + 1\right )}^{2}}} + 18 \, \sqrt {3} e^{\left (\frac {3}{4} \, {\left (2 \, x + 1\right )}^{2}\right )} - 8 \, \sqrt {3} \Gamma \left (2, -\frac {3}{4} \, {\left (2 \, x + 1\right )}^{2}\right )\right )} e^{\left (-\frac {3}{4}\right )} - \frac {1}{24} \, \sqrt {3} {\left (\frac {4 \, {\left (2 \, x + 1\right )}^{3} \Gamma \left (\frac {3}{2}, -\frac {3}{4} \, {\left (2 \, x + 1\right )}^{2}\right )}{\left (-{\left (2 \, x + 1\right )}^{2}\right )^{\frac {3}{2}}} - \frac {3 \, \sqrt {\pi } {\left (2 \, x + 1\right )} {\left (\operatorname {erf}\left (\frac {1}{2} \, \sqrt {3} \sqrt {-{\left (2 \, x + 1\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (2 \, x + 1\right )}^{2}}} + 4 \, \sqrt {3} e^{\left (\frac {3}{4} \, {\left (2 \, x + 1\right )}^{2}\right )}\right )} e^{\left (-\frac {3}{4}\right )} - \frac {1}{18} \, \sqrt {3} {\left (\frac {3 \, \sqrt {\pi } {\left (2 \, x + 1\right )} {\left (\operatorname {erf}\left (\frac {1}{2} \, \sqrt {3} \sqrt {-{\left (2 \, x + 1\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (2 \, x + 1\right )}^{2}}} - 2 \, \sqrt {3} e^{\left (\frac {3}{4} \, {\left (2 \, x + 1\right )}^{2}\right )}\right )} e^{\left (-\frac {3}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.64, size = 14, normalized size = 1.17 \begin {gather*} x^2\,{\mathrm {e}}^{3\,x^2+3\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 1.00 \begin {gather*} x^{2} e^{3 x^{2} + 3 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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