Optimal. Leaf size=35 \[ \frac {e^x x}{(3+x)^2-\frac {2+e^{x^2}}{x \log \left (-x+x^2\right )}} \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Aborted
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Mathematica [A] time = 0.19, size = 37, normalized size = 1.06 \begin {gather*} \frac {e^x x^2 \log ((-1+x) x)}{-2-e^{x^2}+x (3+x)^2 \log ((-1+x) x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 60, normalized size = 1.71 \begin {gather*} \frac {x^{2} e^{\left (x^{2} + x\right )} \log \left (x^{2} - x\right )}{{\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right ) - e^{\left (2 \, x^{2}\right )} - 2 \, e^{\left (x^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.90, size = 72, normalized size = 2.06 \begin {gather*} \frac {x^{2} e^{x} \log \left (x - 1\right ) + x^{2} e^{x} \log \relax (x)}{x^{3} \log \left (x - 1\right ) + x^{3} \log \relax (x) + 6 \, x^{2} \log \left (x - 1\right ) + 6 \, x^{2} \log \relax (x) + 9 \, x \log \left (x - 1\right ) + 9 \, x \log \relax (x) - e^{\left (x^{2}\right )} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.90, size = 348, normalized size = 9.94
method | result | size |
risch | \(\frac {x \,{\mathrm e}^{x}}{\left (3+x \right )^{2}}-\frac {2 x \,{\mathrm e}^{x} \left ({\mathrm e}^{x^{2}}+2\right )}{\left (x^{2}+6 x +9\right ) \left (-i \pi \,x^{3} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}+6 i \pi \,x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}+i \pi \,x^{3} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}+i \pi \,x^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )+9 i \pi x \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}-i \pi \,x^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}+9 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )-9 i \pi x \,\mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}-6 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}+6 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )-9 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}-6 i \pi \,x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}-2 x^{3} \ln \relax (x )-2 x^{3} \ln \left (x -1\right )-12 x^{2} \ln \relax (x )-12 x^{2} \ln \left (x -1\right )-18 x \ln \relax (x )-18 \ln \left (x -1\right ) x +2 \,{\mathrm e}^{x^{2}}+4\right )}\) | \(348\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 62, normalized size = 1.77 \begin {gather*} \frac {x^{2} e^{x} \log \left (x - 1\right ) + x^{2} e^{x} \log \relax (x)}{{\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} \log \left (x - 1\right ) + {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} \log \relax (x) - e^{\left (x^{2}\right )} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^x\,\left (x^6+4\,x^5+4\,x^4-9\,x^2\right )\,{\ln \left (x^2-x\right )}^2+\left ({\mathrm {e}}^{x^2}\,{\mathrm {e}}^x\,\left (2\,x^4-3\,x^3-x^2+2\,x\right )-{\mathrm {e}}^x\,\left (2\,x^3+2\,x^2-4\,x\right )\right )\,\ln \left (x^2-x\right )+{\mathrm {e}}^x\,\left (2\,x-4\,x^2\right )+{\mathrm {e}}^{x^2}\,{\mathrm {e}}^x\,\left (x-2\,x^2\right )}{\left (x^7+11\,x^6+42\,x^5+54\,x^4-27\,x^3-81\,x^2\right )\,{\ln \left (x^2-x\right )}^2+\left (36\,x-{\mathrm {e}}^{x^2}\,\left (2\,x^4+10\,x^3+6\,x^2-18\,x\right )-12\,x^2-20\,x^3-4\,x^4\right )\,\ln \left (x^2-x\right )+4\,x+{\mathrm {e}}^{2\,x^2}\,\left (x-1\right )+{\mathrm {e}}^{x^2}\,\left (4\,x-4\right )-4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.59, size = 53, normalized size = 1.51 \begin {gather*} - \frac {x^{2} e^{x} \log {\left (x^{2} - x \right )}}{- x^{3} \log {\left (x^{2} - x \right )} - 6 x^{2} \log {\left (x^{2} - x \right )} - 9 x \log {\left (x^{2} - x \right )} + e^{x^{2}} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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