Optimal. Leaf size=18 \[ 6-x^2 \left (e^2 x+e^{10} x\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.72, number of steps
used = 3, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {6, 12, 30}
\begin {gather*} -e^2 \left (1+e^8\right ) x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int -3 \left (e^2+e^{10}\right ) x^2 \, dx\\ &=-\left (\left (3 e^2 \left (1+e^8\right )\right ) \int x^2 \, dx\right )\\ &=-e^2 \left (1+e^8\right ) x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 0.94 \begin {gather*} -e^2 x^3-e^{10} x^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 13, normalized size = 0.72
method | result | size |
gosper | \(-x^{3} \left ({\mathrm e}^{10}+{\mathrm e}^{2}\right )\) | \(13\) |
default | \(-x^{3} \left ({\mathrm e}^{10}+{\mathrm e}^{2}\right )\) | \(13\) |
norman | \(\left (-{\mathrm e}^{10}-{\mathrm e}^{2}\right ) x^{3}\) | \(16\) |
risch | \(-x^{3} {\mathrm e}^{10}-x^{3} {\mathrm e}^{2}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 15, normalized size = 0.83 \begin {gather*} -x^{3} e^{10} - x^{3} e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 15, normalized size = 0.83 \begin {gather*} -x^{3} e^{10} - x^{3} e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 10, normalized size = 0.56 \begin {gather*} x^{3} \left (- e^{10} - e^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 15, normalized size = 0.83 \begin {gather*} -x^{3} e^{10} - x^{3} e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.41, size = 11, normalized size = 0.61 \begin {gather*} -x^3\,{\mathrm {e}}^2\,\left ({\mathrm {e}}^8+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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