Optimal. Leaf size=20 \[ e^3+\left (-e^9+x-2 x^3+\log (2)\right )^2 \]
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Rubi [A]
time = 0.01, antiderivative size = 40, normalized size of antiderivative = 2.00, number of steps
used = 3, number of rules used = 0, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} 4 x^6-4 x^4+4 e^9 x^3-4 x^3 \log (2)+x^2-2 e^9 x+2 x \log (2) \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x^2-4 x^4+4 x^6+e^9 \int \left (-2+12 x^2\right ) \, dx+\log (2) \int \left (2-12 x^2\right ) \, dx\\ &=-2 e^9 x+x^2+4 e^9 x^3-4 x^4+4 x^6+2 x \log (2)-4 x^3 \log (2)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 1.35 \begin {gather*} x \left (-1+2 x^2\right ) \left (2 e^9-x+2 x^3-\log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.68, size = 16, normalized size = 0.80
method | result | size |
default | \(\left (x +\ln \left (2\right )-{\mathrm e}^{9}-2 x^{3}\right )^{2}\) | \(16\) |
norman | \(x^{2}+\left (-4 \ln \left (2\right )+4 \,{\mathrm e}^{9}\right ) x^{3}+\left (2 \ln \left (2\right )-2 \,{\mathrm e}^{9}\right ) x -4 x^{4}+4 x^{6}\) | \(39\) |
risch | \(-4 x^{3} \ln \left (2\right )+2 x \ln \left (2\right )+4 x^{3} {\mathrm e}^{9}-2 x \,{\mathrm e}^{9}+4 x^{6}-4 x^{4}+x^{2}\) | \(39\) |
gosper | \(-x \left (-4 x^{5}+4 x^{2} \ln \left (2\right )-4 x^{2} {\mathrm e}^{9}+4 x^{3}-2 \ln \left (2\right )+2 \,{\mathrm e}^{9}-x \right )\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 40, normalized size = 2.00 \begin {gather*} 4 \, x^{6} - 4 \, x^{4} + x^{2} + 2 \, {\left (2 \, x^{3} - x\right )} e^{9} - 2 \, {\left (2 \, x^{3} - x\right )} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 40, normalized size = 2.00 \begin {gather*} 4 \, x^{6} - 4 \, x^{4} + x^{2} + 2 \, {\left (2 \, x^{3} - x\right )} e^{9} - 2 \, {\left (2 \, x^{3} - x\right )} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 37 vs.
\(2 (17) = 34\).
time = 0.01, size = 37, normalized size = 1.85 \begin {gather*} 4 x^{6} - 4 x^{4} + x^{3} \left (- 4 \log {\left (2 \right )} + 4 e^{9}\right ) + x^{2} + x \left (- 2 e^{9} + 2 \log {\left (2 \right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 40, normalized size = 2.00 \begin {gather*} 4 \, x^{6} - 4 \, x^{4} + x^{2} + 2 \, {\left (2 \, x^{3} - x\right )} e^{9} - 2 \, {\left (2 \, x^{3} - x\right )} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 39, normalized size = 1.95 \begin {gather*} 4\,x^6-4\,x^4+\left (4\,{\mathrm {e}}^9-4\,\ln \left (2\right )\right )\,x^3+x^2+\left (\ln \left (4\right )-2\,{\mathrm {e}}^9\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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