Optimal. Leaf size=27 \[ \frac {5}{2-e^{x^2} \left (x+x \log \left (-x+x^2\right )\right )^2} \]
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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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Rubi steps
Aborted
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Mathematica [A]
time = 0.08, size = 48, normalized size = 1.78 \begin {gather*} -\frac {5}{-2+e^{x^2} x^2+2 e^{x^2} x^2 \log ((-1+x) x)+e^{x^2} x^2 \log ^2((-1+x) x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.80, size = 703, normalized size = 26.04
method | result | size |
risch | \(\frac {20}{8-8 x^{2} {\mathrm e}^{x^{2}} \ln \left (x \right )-4 x^{2} {\mathrm e}^{x^{2}}+4 i {\mathrm e}^{x^{2}} \pi \,x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right ) \mathrm {csgn}\left (i x \right ) \ln \left (x \right )+4 i {\mathrm e}^{x^{2}} \pi \,x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right ) \mathrm {csgn}\left (i x \right ) \ln \left (x -1\right )+4 i \pi \,x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} {\mathrm e}^{x^{2}}+{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4}+{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4} \mathrm {csgn}\left (i x \right )^{2}-2 \,{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5}-2 \,{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5} \mathrm {csgn}\left (i x \right )+{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{6}+{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \right )^{2}-2 \,{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \mathrm {csgn}\left (i x \right )+4 i {\mathrm e}^{x^{2}} \pi \,x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \left (x \right )-4 i \pi \,x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} {\mathrm e}^{x^{2}}-4 i \pi \,x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \right ) {\mathrm e}^{x^{2}}+4 i {\mathrm e}^{x^{2}} \pi \,x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \left (x -1\right )-2 \,{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \mathrm {csgn}\left (i x \right )^{2}-8 \,{\mathrm e}^{x^{2}} x^{2} \ln \left (x \right ) \ln \left (x -1\right )-4 \,{\mathrm e}^{x^{2}} x^{2} \ln \left (x \right )^{2}-4 \,{\mathrm e}^{x^{2}} x^{2} \ln \left (x -1\right )^{2}-8 x^{2} {\mathrm e}^{x^{2}} \ln \left (x -1\right )+4 \,{\mathrm e}^{x^{2}} \pi ^{2} x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4} \mathrm {csgn}\left (i x \right )-4 i {\mathrm e}^{x^{2}} \pi \,x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \left (x \right )+4 i \pi \,x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right ) \mathrm {csgn}\left (i x \right ) {\mathrm e}^{x^{2}}-4 i {\mathrm e}^{x^{2}} \pi \,x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \right ) \ln \left (x -1\right )-4 i {\mathrm e}^{x^{2}} \pi \,x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \left (x -1\right )-4 i {\mathrm e}^{x^{2}} \pi \,x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \right ) \ln \left (x \right )}\) | \(703\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 56 vs.
\(2 (25) = 50\).
time = 0.45, size = 56, normalized size = 2.07 \begin {gather*} -\frac {5}{{\left (x^{2} \log \left (x - 1\right )^{2} + x^{2} \log \left (x\right )^{2} + 2 \, x^{2} \log \left (x\right ) + x^{2} + 2 \, {\left (x^{2} \log \left (x\right ) + x^{2}\right )} \log \left (x - 1\right )\right )} e^{\left (x^{2}\right )} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 49, normalized size = 1.81 \begin {gather*} -\frac {5}{x^{2} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right )^{2} + 2 \, x^{2} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right ) + x^{2} e^{\left (x^{2}\right )} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.26, size = 36, normalized size = 1.33 \begin {gather*} - \frac {5}{\left (x^{2} \log {\left (x^{2} - x \right )}^{2} + 2 x^{2} \log {\left (x^{2} - x \right )} + x^{2}\right ) e^{x^{2}} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.72, size = 49, normalized size = 1.81 \begin {gather*} -\frac {5}{x^{2} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right )^{2} + 2 \, x^{2} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right ) + x^{2} 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 = -0.04 \begin {gather*} -\int \frac {{\mathrm {e}}^{x^2}\,\left (-10\,x^4+10\,x^3-10\,x^2+10\,x\right )\,{\ln \left (x^2-x\right )}^2+{\mathrm {e}}^{x^2}\,\left (-20\,x^4+20\,x^3-40\,x^2+30\,x\right )\,\ln \left (x^2-x\right )+{\mathrm {e}}^{x^2}\,\left (-10\,x^4+10\,x^3-30\,x^2+20\,x\right )}{-{\mathrm {e}}^{2\,x^2}\,\left (x^4-x^5\right )\,{\ln \left (x^2-x\right )}^4-{\mathrm {e}}^{2\,x^2}\,\left (4\,x^4-4\,x^5\right )\,{\ln \left (x^2-x\right )}^3+\left ({\mathrm {e}}^{x^2}\,\left (4\,x^2-4\,x^3\right )-{\mathrm {e}}^{2\,x^2}\,\left (6\,x^4-6\,x^5\right )\right )\,{\ln \left (x^2-x\right )}^2+\left ({\mathrm {e}}^{x^2}\,\left (8\,x^2-8\,x^3\right )-{\mathrm {e}}^{2\,x^2}\,\left (4\,x^4-4\,x^5\right )\right )\,\ln \left (x^2-x\right )+4\,x-{\mathrm {e}}^{2\,x^2}\,\left (x^4-x^5\right )+{\mathrm {e}}^{x^2}\,\left (4\,x^2-4\,x^3\right )-4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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