Optimal. Leaf size=34 \[ \frac {e^{2 x}}{-3+x+e^{16 \left (3+\frac {3+5 x}{3-x}\right )^2} x} \]
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Rubi [F]
time = 11.19, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {e^{2 x} \left (189-243 x+117 x^2-25 x^3+2 x^4+e^{\frac {2304+768 x+64 x^2}{9-6 x+x^2}} \left (27+6831 x+1215 x^2-19 x^3+2 x^4\right )\right )}{-243+405 x-270 x^2+90 x^3-15 x^4+x^5+e^{\frac {2 \left (2304+768 x+64 x^2\right )}{9-6 x+x^2}} \left (-27 x^2+27 x^3-9 x^4+x^5\right )+e^{\frac {2304+768 x+64 x^2}{9-6 x+x^2}} \left (162 x-216 x^2+108 x^3-24 x^4+2 x^5\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2 x} \left (-(-3+x)^3 (-7+2 x)-e^{\frac {64 (6+x)^2}{(-3+x)^2}} \left (27+6831 x+1215 x^2-19 x^3+2 x^4\right )\right )}{(3-x)^3 \left (3-x-e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2} \, dx\\ &=\int \left (-\frac {3 e^{2 x} \left (9+2298 x+385 x^2\right )}{(-3+x)^2 x \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2}+\frac {e^{2 x} \left (27+6831 x+1215 x^2-19 x^3+2 x^4\right )}{(-3+x)^3 x \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )}\right ) \, dx\\ &=-\left (3 \int \frac {e^{2 x} \left (9+2298 x+385 x^2\right )}{(-3+x)^2 x \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2} \, dx\right )+\int \frac {e^{2 x} \left (27+6831 x+1215 x^2-19 x^3+2 x^4\right )}{(-3+x)^3 x \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )} \, dx\\ &=-\left (3 \int \left (\frac {3456 e^{2 x}}{(-3+x)^2 \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2}+\frac {384 e^{2 x}}{(-3+x) \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2}+\frac {e^{2 x}}{x \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2}\right ) \, dx\right )+\int \left (\frac {2 e^{2 x}}{-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x}+\frac {10368 e^{2 x}}{(-3+x)^3 \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )}+\frac {1152 e^{2 x}}{(-3+x)^2 \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )}-\frac {e^{2 x}}{x \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )}\right ) \, dx\\ &=2 \int \frac {e^{2 x}}{-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x} \, dx-3 \int \frac {e^{2 x}}{x \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2} \, dx-1152 \int \frac {e^{2 x}}{(-3+x) \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2} \, dx+1152 \int \frac {e^{2 x}}{(-3+x)^2 \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )} \, dx-10368 \int \frac {e^{2 x}}{(-3+x)^2 \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )^2} \, dx+10368 \int \frac {e^{2 x}}{(-3+x)^3 \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )} \, dx-\int \frac {e^{2 x}}{x \left (-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.29, size = 27, normalized size = 0.79 \begin {gather*} \frac {e^{2 x}}{-3+x+e^{\frac {64 (6+x)^2}{(-3+x)^2}} x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.27, size = 26, normalized size = 0.76
method | result | size |
risch | \(\frac {{\mathrm e}^{2 x}}{{\mathrm e}^{\frac {64 \left (x +6\right )^{2}}{\left (x -3\right )^{2}}} x +x -3}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 34, normalized size = 1.00 \begin {gather*} \frac {e^{\left (2 \, x\right )}}{x e^{\left (\frac {5184}{x^{2} - 6 \, x + 9} + \frac {1152}{x - 3} + 64\right )} + x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 33, normalized size = 0.97 \begin {gather*} \frac {e^{\left (2 \, x\right )}}{x e^{\left (\frac {64 \, {\left (x^{2} + 12 \, x + 36\right )}}{x^{2} - 6 \, x + 9}\right )} + x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.22, size = 29, normalized size = 0.85 \begin {gather*} \frac {e^{2 x}}{x e^{\frac {64 x^{2} + 768 x + 2304}{x^{2} - 6 x + 9}} + x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.62, size = 34, normalized size = 1.00 \begin {gather*} \frac {e^{\left (2 \, x\right )}}{x e^{\left (-\frac {192 \, {\left (x^{2} - 12 \, x\right )}}{x^{2} - 6 \, x + 9} + 256\right )} + x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.22, size = 116, normalized size = 3.41 \begin {gather*} \frac {{\mathrm {e}}^{2\,x}\,\left (385\,x^2+2298\,x+9\right )\,{\left (x^3-9\,x^2+27\,x-27\right )}^2}{{\left (x-3\right )}^2\,\left (x+x\,{\mathrm {e}}^{\frac {768\,x}{x^2-6\,x+9}+\frac {2304}{x^2-6\,x+9}+\frac {64\,x^2}{x^2-6\,x+9}}-3\right )\,\left (385\,x^6-2322\,x^5-6777\,x^4+82404\,x^3-216513\,x^2+185166\,x+729\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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