Optimal. Leaf size=16 \[ e^{2 x} x \left (7 x-x^2\right ) \]
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Rubi [A] time = 0.10, antiderivative size = 21, normalized size of antiderivative = 1.31, number of steps used = 12, number of rules used = 4, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {1594, 2196, 2176, 2194} \begin {gather*} 7 e^{2 x} x^2-e^{2 x} x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 1594
Rule 2176
Rule 2194
Rule 2196
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{2 x} x \left (14+11 x-2 x^2\right ) \, dx\\ &=\int \left (14 e^{2 x} x+11 e^{2 x} x^2-2 e^{2 x} x^3\right ) \, dx\\ &=-\left (2 \int e^{2 x} x^3 \, dx\right )+11 \int e^{2 x} x^2 \, dx+14 \int e^{2 x} x \, dx\\ &=7 e^{2 x} x+\frac {11}{2} e^{2 x} x^2-e^{2 x} x^3+3 \int e^{2 x} x^2 \, dx-7 \int e^{2 x} \, dx-11 \int e^{2 x} x \, dx\\ &=-\frac {7 e^{2 x}}{2}+\frac {3}{2} e^{2 x} x+7 e^{2 x} x^2-e^{2 x} x^3-3 \int e^{2 x} x \, dx+\frac {11}{2} \int e^{2 x} \, dx\\ &=-\frac {3 e^{2 x}}{4}+7 e^{2 x} x^2-e^{2 x} x^3+\frac {3}{2} \int e^{2 x} \, dx\\ &=7 e^{2 x} x^2-e^{2 x} x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 13, normalized size = 0.81 \begin {gather*} -e^{2 x} (-7+x) x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 15, normalized size = 0.94 \begin {gather*} -{\left (x^{3} - 7 \, x^{2}\right )} e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 15, normalized size = 0.94 \begin {gather*} -{\left (x^{3} - 7 \, x^{2}\right )} e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 0.81
method | result | size |
gosper | \(-{\mathrm e}^{2 x} \left (x -7\right ) x^{2}\) | \(13\) |
risch | \(\left (-x^{3}+7 x^{2}\right ) {\mathrm e}^{2 x}\) | \(17\) |
default | \(7 \,{\mathrm e}^{2 x} x^{2}-{\mathrm e}^{2 x} x^{3}\) | \(20\) |
norman | \(7 \,{\mathrm e}^{2 x} x^{2}-{\mathrm e}^{2 x} x^{3}\) | \(20\) |
meijerg | \(\frac {\left (-32 x^{3}+48 x^{2}-48 x +24\right ) {\mathrm e}^{2 x}}{32}+\frac {11 \left (12 x^{2}-12 x +6\right ) {\mathrm e}^{2 x}}{24}-\frac {7 \left (-4 x +2\right ) {\mathrm e}^{2 x}}{4}\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.35, size = 49, normalized size = 3.06 \begin {gather*} -\frac {1}{4} \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x\right )} + \frac {11}{4} \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} + \frac {7}{2} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 12, normalized size = 0.75 \begin {gather*} -x^2\,{\mathrm {e}}^{2\,x}\,\left (x-7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.75 \begin {gather*} \left (- x^{3} + 7 x^{2}\right ) e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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