Optimal. Leaf size=32 \[ \frac {e^{-\left (1+\log (4)-\log \left (x^2\right )\right )^2}}{2 \left (-5+\frac {3}{x}+x+\log (x)\right )} \]
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Rubi [B] time = 0.88, antiderivative size = 87, normalized size of antiderivative = 2.72, number of steps used = 4, number of rules used = 4, integrand size = 137, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {12, 2274, 15, 2288} \begin {gather*} \frac {x^5 e^{-\log ^2\left (x^2\right )-1-\log ^2(4)} \left (x^2\right )^{\log (16)} \left (x^2-5 x+x \log (x)+3\right )}{32 \left (x^4-10 x^3+31 x^2+x^2 \log ^2(x)+2 \left (x^3-5 x^2+3 x\right ) \log (x)-30 x+9\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 15
Rule 2274
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int \frac {\exp \left (-1-\log ^2(4)-(-2-2 \log (4)) \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \left (15-21 x+3 x^2+\left (12-20 x+4 x^2\right ) \log (4)+(4 x+4 x \log (4)) \log (x)+\left (-12+20 x-4 x^2-4 x \log (x)\right ) \log \left (x^2\right )\right )}{18-60 x+62 x^2-20 x^3+2 x^4+\left (12 x-20 x^2+4 x^3\right ) \log (x)+2 x^2 \log ^2(x)} \, dx\\ &=\frac {1}{16} \int \frac {e^{-1-\log ^2(4)-\log ^2\left (x^2\right )} \left (x^2\right )^{2+2 \log (4)} \left (15-21 x+3 x^2+\left (12-20 x+4 x^2\right ) \log (4)+(4 x+4 x \log (4)) \log (x)+\left (-12+20 x-4 x^2-4 x \log (x)\right ) \log \left (x^2\right )\right )}{18-60 x+62 x^2-20 x^3+2 x^4+\left (12 x-20 x^2+4 x^3\right ) \log (x)+2 x^2 \log ^2(x)} \, dx\\ &=\frac {1}{16} \left (x^{-4 \log (4)} \left (x^2\right )^{2 \log (4)}\right ) \int \frac {e^{-1-\log ^2(4)-\log ^2\left (x^2\right )} x^{2 (2+2 \log (4))} \left (15-21 x+3 x^2+\left (12-20 x+4 x^2\right ) \log (4)+(4 x+4 x \log (4)) \log (x)+\left (-12+20 x-4 x^2-4 x \log (x)\right ) \log \left (x^2\right )\right )}{18-60 x+62 x^2-20 x^3+2 x^4+\left (12 x-20 x^2+4 x^3\right ) \log (x)+2 x^2 \log ^2(x)} \, dx\\ &=\frac {e^{-1-\log ^2(4)-\log ^2\left (x^2\right )} x^5 \left (x^2\right )^{\log (16)} \left (3-5 x+x^2+x \log (x)\right )}{32 \left (9-30 x+31 x^2-10 x^3+x^4+2 \left (3 x-5 x^2+x^3\right ) \log (x)+x^2 \log ^2(x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 2.20, size = 140, normalized size = 4.38 \begin {gather*} \frac {1}{16} \int \frac {e^{-1-\log ^2(4)-(-2-2 \log (4)) \log \left (x^2\right )-\log ^2\left (x^2\right )} \left (15-21 x+3 x^2+\left (12-20 x+4 x^2\right ) \log (4)+(4 x+4 x \log (4)) \log (x)+\left (-12+20 x-4 x^2-4 x \log (x)\right ) \log \left (x^2\right )\right )}{18-60 x+62 x^2-20 x^3+2 x^4+\left (12 x-20 x^2+4 x^3\right ) \log (x)+2 x^2 \log ^2(x)} \, dx \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.19, size = 46, normalized size = 1.44 \begin {gather*} \frac {x e^{\left (-4 \, \log \relax (2)^{2} + 4 \, {\left (2 \, \log \relax (2) + 1\right )} \log \relax (x) - 4 \, \log \relax (x)^{2} - 4 \, \log \relax (2) - 1\right )}}{2 \, {\left (x^{2} + x \log \relax (x) - 5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.47, size = 42, normalized size = 1.31 \begin {gather*} \frac {x e^{\left (-4 \, \log \relax (2)^{2} + 8 \, \log \relax (2) \log \relax (x) - 4 \, \log \relax (x)^{2} + 4 \, \log \relax (x) - 1\right )}}{32 \, {\left (x^{2} + x \log \relax (x) - 5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.79, size = 244, normalized size = 7.62
method | result | size |
risch | \(\frac {x^{5} x^{8 \ln \relax (2)} x^{-4 i \pi \,\mathrm {csgn}\left (i x \right )} 2^{4 i \pi \,\mathrm {csgn}\left (i x \right )} 2^{-4 i \pi \,\mathrm {csgn}\left (i x^{2}\right )} x^{4 i \pi \,\mathrm {csgn}\left (i x^{2}\right )} {\mathrm e}^{-4 \ln \relax (x )^{2}-1+\frac {\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}}{4}-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right )+\frac {3 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}}{2}-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3}+\frac {\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4}}{4}-i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}+2 i \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-4 \ln \relax (2)^{2}}}{32 x \ln \relax (x )+32 x^{2}-160 x +96}\) | \(244\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.82, size = 71, normalized size = 2.22 \begin {gather*} \frac {x^{5} e^{\left (8 \, \log \relax (2) \log \relax (x) - 4 \, \log \relax (x)^{2}\right )}}{32 \, {\left (x^{2} e^{\left (4 \, \log \relax (2)^{2} + 1\right )} + x e^{\left (4 \, \log \relax (2)^{2} + 1\right )} \log \relax (x) - 5 \, x e^{\left (4 \, \log \relax (2)^{2} + 1\right )} + 3 \, e^{\left (4 \, \log \relax (2)^{2} + 1\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.20, size = 47, normalized size = 1.47 \begin {gather*} \frac {x^5\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-{\ln \left (x^2\right )}^2}\,{\mathrm {e}}^{-4\,{\ln \relax (2)}^2}\,{\left (x^2\right )}^{4\,\ln \relax (2)}}{32\,\left (x\,\ln \relax (x)-5\,x+x^2+3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [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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