Optimal. Leaf size=19 \[ x \log \left (4 e^{\left (3+x^6\right )^2} (3-x)\right ) \]
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Rubi [A] time = 0.18, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 7, number of rules used = 3, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {6742, 1620, 2548} \begin {gather*} x \log \left (4 e^{\left (x^6+3\right )^2} (3-x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1620
Rule 2548
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {x \left (-1+108 x^5-36 x^6+36 x^{11}-12 x^{12}\right )}{3-x}+\log \left (-4 e^{\left (3+x^6\right )^2} (-3+x)\right )\right ) \, dx\\ &=\int \frac {x \left (-1+108 x^5-36 x^6+36 x^{11}-12 x^{12}\right )}{3-x} \, dx+\int \log \left (-4 e^{\left (3+x^6\right )^2} (-3+x)\right ) \, dx\\ &=x \log \left (4 e^{\left (3+x^6\right )^2} (3-x)\right )-\int \frac {x \left (-1+108 x^5-36 x^6+36 x^{11}-12 x^{12}\right )}{3-x} \, dx+\int \left (1+\frac {3}{-3+x}+36 x^6+12 x^{12}\right ) \, dx\\ &=x+\frac {36 x^7}{7}+\frac {12 x^{13}}{13}+3 \log (3-x)+x \log \left (4 e^{\left (3+x^6\right )^2} (3-x)\right )-\int \left (1+\frac {3}{-3+x}+36 x^6+12 x^{12}\right ) \, dx\\ &=x \log \left (4 e^{\left (3+x^6\right )^2} (3-x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 17, normalized size = 0.89 \begin {gather*} x \log \left (-4 e^{\left (3+x^6\right )^2} (-3+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 19, normalized size = 1.00 \begin {gather*} x \log \left (-4 \, {\left (x - 3\right )} e^{\left (x^{12} + 6 \, x^{6} + 9\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 20, normalized size = 1.05 \begin {gather*} x^{13} + 6 \, x^{7} + x \log \left (-4 \, x + 12\right ) + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.45, size = 21, normalized size = 1.11
method | result | size |
default | \(x \ln \left (\left (-4 x +12\right ) {\mathrm e}^{x^{12}+6 x^{6}+9}\right )\) | \(21\) |
risch | \(x \ln \left ({\mathrm e}^{\left (x^{6}+3\right )^{2}}\right )+\ln \left (x -3\right ) x -i x \pi \mathrm {csgn}\left (i \left (x -3\right ) {\mathrm e}^{\left (x^{6}+3\right )^{2}}\right )^{2}-\frac {i x \pi \,\mathrm {csgn}\left (i \left (x -3\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{\left (x^{6}+3\right )^{2}}\right ) \mathrm {csgn}\left (i \left (x -3\right ) {\mathrm e}^{\left (x^{6}+3\right )^{2}}\right )}{2}+\frac {i x \pi \,\mathrm {csgn}\left (i \left (x -3\right )\right ) \mathrm {csgn}\left (i \left (x -3\right ) {\mathrm e}^{\left (x^{6}+3\right )^{2}}\right )^{2}}{2}+\frac {i x \pi \,\mathrm {csgn}\left (i {\mathrm e}^{\left (x^{6}+3\right )^{2}}\right ) \mathrm {csgn}\left (i \left (x -3\right ) {\mathrm e}^{\left (x^{6}+3\right )^{2}}\right )^{2}}{2}+\frac {i x \pi \mathrm {csgn}\left (i \left (x -3\right ) {\mathrm e}^{\left (x^{6}+3\right )^{2}}\right )^{3}}{2}+i x \pi +2 x \ln \relax (2)\) | \(175\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.75, size = 84, normalized size = 4.42 \begin {gather*} {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (-4 \, x e^{\left (x^{12} + 6 \, x^{6} + 9\right )} + 12 \, e^{\left (x^{12} + 6 \, x^{6} + 9\right )}\right ) + 3 \, {\left (-i \, \pi - 2 \, \log \relax (2) - 535824\right )} \log \left (x - 3\right ) - 3 \, {\left (x^{12} + 6 \, x^{6} - 535814\right )} \log \left (x - 3\right ) - 3 \, \log \left (x - 3\right )^{2} + 3 \, \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.72, size = 18, normalized size = 0.95 \begin {gather*} x\,\left (\ln \left (12-4\,x\right )+6\,x^6+x^{12}+9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.58, size = 42, normalized size = 2.21 \begin {gather*} \frac {3 x^{12}}{2} + 9 x^{6} + \left (x - \frac {3}{2}\right ) \log {\left (\left (12 - 4 x\right ) e^{x^{12} + 6 x^{6} + 9} \right )} + \frac {3 \log {\left (x - 3 \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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