Optimal. Leaf size=22 \[ x+\frac {2 x^2}{25 \left (e^3-3 (3-2 x)\right )^4} \]
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Rubi [B] time = 0.27, antiderivative size = 66, normalized size of antiderivative = 3.00, number of steps used = 2, number of rules used = 1, integrand size = 195, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {2074} \begin {gather*} x+\frac {1}{450 \left (-6 x-e^3+9\right )^2}-\frac {9-e^3}{225 \left (-6 x-e^3+9\right )^3}+\frac {\left (9-e^3\right )^2}{450 \left (-6 x-e^3+9\right )^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {4 \left (-9+e^3\right )^2}{75 \left (-9+e^3+6 x\right )^5}+\frac {2 \left (-9+e^3\right )}{25 \left (-9+e^3+6 x\right )^4}-\frac {2}{75 \left (-9+e^3+6 x\right )^3}\right ) \, dx\\ &=\frac {\left (9-e^3\right )^2}{450 \left (9-e^3-6 x\right )^4}-\frac {9-e^3}{225 \left (9-e^3-6 x\right )^3}+\frac {1}{450 \left (9-e^3-6 x\right )^2}+x\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.05, size = 60, normalized size = 2.73 \begin {gather*} \frac {81-e^6+6 e^3 (3-2 x)+54 (-3+2 x)+\left (-9+e^3+6 x\right )^2+75 \left (-9+e^3+6 x\right )^5}{450 \left (-9+e^3+6 x\right )^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.76, size = 151, normalized size = 6.86 \begin {gather*} \frac {32400 \, x^{5} - 194400 \, x^{4} + 437400 \, x^{3} - 437398 \, x^{2} + 25 \, x e^{12} + 300 \, {\left (2 \, x^{2} - 3 \, x\right )} e^{9} + 1350 \, {\left (4 \, x^{3} - 12 \, x^{2} + 9 \, x\right )} e^{6} + 2700 \, {\left (8 \, x^{4} - 36 \, x^{3} + 54 \, x^{2} - 27 \, x\right )} e^{3} + 164025 \, x}{25 \, {\left (1296 \, x^{4} - 7776 \, x^{3} + 17496 \, x^{2} + 12 \, {\left (2 \, x - 3\right )} e^{9} + 54 \, {\left (4 \, x^{2} - 12 \, x + 9\right )} e^{6} + 108 \, {\left (8 \, x^{3} - 36 \, x^{2} + 54 \, x - 27\right )} e^{3} - 17496 \, x + e^{12} + 6561\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.43, size = 80, normalized size = 3.64
method | result | size |
risch | \(x +\frac {2 x^{2}}{25 \left ({\mathrm e}^{12}+24 x \,{\mathrm e}^{9}+216 x^{2} {\mathrm e}^{6}+864 x^{3} {\mathrm e}^{3}+1296 x^{4}-36 \,{\mathrm e}^{9}-648 x \,{\mathrm e}^{6}-3888 x^{2} {\mathrm e}^{3}-7776 x^{3}+486 \,{\mathrm e}^{6}+5832 x \,{\mathrm e}^{3}+17496 x^{2}-2916 \,{\mathrm e}^{3}-17496 x +6561\right )}\) | \(80\) |
norman | \(\frac {\left (-360 \,{\mathrm e}^{6}+6480 \,{\mathrm e}^{3}-29160\right ) x^{3}+\left (-120 \,{\mathrm e}^{9}+3240 \,{\mathrm e}^{6}-29160 \,{\mathrm e}^{3}+\frac {2187002}{25}\right ) x^{2}+\left (-15 \,{\mathrm e}^{12}+540 \,{\mathrm e}^{9}-7290 \,{\mathrm e}^{6}+43740 \,{\mathrm e}^{3}-98415\right ) x +1296 x^{5}-\frac {2 \,{\mathrm e}^{15}}{3}+30 \,{\mathrm e}^{12}-540 \,{\mathrm e}^{9}+4860 \,{\mathrm e}^{6}-21870 \,{\mathrm e}^{3}+39366}{\left ({\mathrm e}^{3}+6 x -9\right )^{4}}\) | \(110\) |
default | \(x +\frac {2 \left (\munderset {\textit {\_R} =\RootOf \left (7776 \textit {\_Z}^{5}+\left (6480 \,{\mathrm e}^{3}-58320\right ) \textit {\_Z}^{4}+\left (-38880 \,{\mathrm e}^{3}+2160 \,{\mathrm e}^{6}+174960\right ) \textit {\_Z}^{3}+\left (87480 \,{\mathrm e}^{3}+360 \,{\mathrm e}^{9}-9720 \,{\mathrm e}^{6}-262440\right ) \textit {\_Z}^{2}+\left (-87480 \,{\mathrm e}^{3}+30 \,{\mathrm e}^{12}-1080 \,{\mathrm e}^{9}+14580 \,{\mathrm e}^{6}+196830\right ) \textit {\_Z} +32805 \,{\mathrm e}^{3}+{\mathrm e}^{15}-45 \,{\mathrm e}^{12}+810 \,{\mathrm e}^{9}-7290 \,{\mathrm e}^{6}-59049\right )}{\sum }\frac {\left (-6 \textit {\_R}^{2}+\left ({\mathrm e}^{3}-9\right ) \textit {\_R} \right ) \ln \left (x -\textit {\_R} \right )}{6561+{\mathrm e}^{12}+24 \textit {\_R} \,{\mathrm e}^{9}+216 \textit {\_R}^{2} {\mathrm e}^{6}+864 \textit {\_R}^{3} {\mathrm e}^{3}+1296 \textit {\_R}^{4}-36 \,{\mathrm e}^{9}-648 \textit {\_R} \,{\mathrm e}^{6}-3888 \textit {\_R}^{2} {\mathrm e}^{3}-7776 \textit {\_R}^{3}+486 \,{\mathrm e}^{6}+5832 \textit {\_R} \,{\mathrm e}^{3}+17496 \textit {\_R}^{2}-2916 \,{\mathrm e}^{3}-17496 \textit {\_R}}\right )}{375}\) | \(187\) |
gosper | \(-\frac {50 \,{\mathrm e}^{15}+1125 x \,{\mathrm e}^{12}+9000 x^{2} {\mathrm e}^{9}+27000 x^{3} {\mathrm e}^{6}-97200 x^{5}-2250 \,{\mathrm e}^{12}-40500 x \,{\mathrm e}^{9}-243000 x^{2} {\mathrm e}^{6}-486000 x^{3} {\mathrm e}^{3}+40500 \,{\mathrm e}^{9}+546750 x \,{\mathrm e}^{6}+2187000 x^{2} {\mathrm e}^{3}+2187000 x^{3}-364500 \,{\mathrm e}^{6}-3280500 x \,{\mathrm e}^{3}-6561006 x^{2}+1640250 \,{\mathrm e}^{3}+7381125 x -2952450}{75 \left ({\mathrm e}^{12}+24 x \,{\mathrm e}^{9}+216 x^{2} {\mathrm e}^{6}+864 x^{3} {\mathrm e}^{3}+1296 x^{4}-36 \,{\mathrm e}^{9}-648 x \,{\mathrm e}^{6}-3888 x^{2} {\mathrm e}^{3}-7776 x^{3}+486 \,{\mathrm e}^{6}+5832 x \,{\mathrm e}^{3}+17496 x^{2}-2916 \,{\mathrm e}^{3}-17496 x +6561\right )}\) | \(202\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 67, normalized size = 3.05 \begin {gather*} x + \frac {2 \, x^{2}}{25 \, {\left (1296 \, x^{4} + 864 \, x^{3} {\left (e^{3} - 9\right )} + 216 \, x^{2} {\left (e^{6} - 18 \, e^{3} + 81\right )} + 24 \, x {\left (e^{9} - 27 \, e^{6} + 243 \, e^{3} - 729\right )} + e^{12} - 36 \, e^{9} + 486 \, e^{6} - 2916 \, e^{3} + 6561\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.33, size = 84, normalized size = 3.82 \begin {gather*} \frac {x\,\left (12150\,{\mathrm {e}}^6-72900\,{\mathrm {e}}^3-437398\,x-900\,{\mathrm {e}}^9+25\,{\mathrm {e}}^{12}+145800\,x\,{\mathrm {e}}^3-16200\,x\,{\mathrm {e}}^6+600\,x\,{\mathrm {e}}^9-97200\,x^2\,{\mathrm {e}}^3+21600\,x^3\,{\mathrm {e}}^3+5400\,x^2\,{\mathrm {e}}^6+437400\,x^2-194400\,x^3+32400\,x^4+164025\right )}{25\,{\left (6\,x+{\mathrm {e}}^3-9\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.83, size = 76, normalized size = 3.45 \begin {gather*} \frac {2 x^{2}}{32400 x^{4} + x^{3} \left (-194400 + 21600 e^{3}\right ) + x^{2} \left (- 97200 e^{3} + 437400 + 5400 e^{6}\right ) + x \left (- 16200 e^{6} - 437400 + 145800 e^{3} + 600 e^{9}\right ) - 900 e^{9} - 72900 e^{3} + 164025 + 25 e^{12} + 12150 e^{6}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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