Optimal. Leaf size=12 \[ \left (-1-e^4+3 x\right )^2 \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.17, number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 9 x^2-6 \left (1+e^4\right ) x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-6 \left (1+e^4\right ) x+9 x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.25 \begin {gather*} -6 x-6 e^4 x+9 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 14, normalized size = 1.17 \begin {gather*} 9 \, x^{2} - 6 \, x e^{4} - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 2.24, size = 14, normalized size = 1.17 \begin {gather*} 9 \, x^{2} - 6 \, x e^{4} - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 1.08
method | result | size |
gosper | \(-3 x \left (-3 x +2 \,{\mathrm e}^{4}+2\right )\) | \(13\) |
default | \(-6 x \,{\mathrm e}^{4}+9 x^{2}-6 x\) | \(15\) |
norman | \(\left (-6 \,{\mathrm e}^{4}-6\right ) x +9 x^{2}\) | \(15\) |
risch | \(-6 x \,{\mathrm e}^{4}+9 x^{2}-6 x\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 14, normalized size = 1.17 \begin {gather*} 9 \, x^{2} - 6 \, x e^{4} - 6 \, x \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 = 1.00 \begin {gather*} -3\,x\,\left (2\,{\mathrm {e}}^4-3\,x+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 14, normalized size = 1.17 \begin {gather*} 9 x^{2} + x \left (- 6 e^{4} - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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