Optimal. Leaf size=26 \[ e^{x+\left (\frac {2}{x}+x+\log \left (e^{4/5} x\right )\right ) \log ^2\left (x^2\right )} \]
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Rubi [F] time = 7.31, 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 {\exp \left (\frac {x^2+\left (2+x^2\right ) \log ^2\left (x^2\right )+x \log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )}{x}\right ) \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \left (x^2+\left (8+4 x^2\right ) \log \left (x^2\right )+4 x \log \left (e^{4/5} x\right ) \log \left (x^2\right )+\left (-2+x+x^2\right ) \log ^2\left (x^2\right )\right )}{x^2} \, dx\\ &=\int \left (\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right )+\frac {4 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \left (10+4 x+5 x^2+5 x \log (x)\right ) \log \left (x^2\right )}{5 x^2}+\frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) (-1+x) (2+x) \log ^2\left (x^2\right )}{x^2}\right ) \, dx\\ &=\frac {4}{5} \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \left (10+4 x+5 x^2+5 x \log (x)\right ) \log \left (x^2\right )}{x^2} \, dx+\int \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \, dx+\int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) (-1+x) (2+x) \log ^2\left (x^2\right )}{x^2} \, dx\\ &=\frac {4}{5} \int \left (5 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )+\frac {10 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^2}+\frac {4 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x}+\frac {5 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log (x) \log \left (x^2\right )}{x}\right ) \, dx+\int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \, dx+\int \left (\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )-\frac {2 \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x^2}+\frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x}\right ) \, dx\\ &=-\left (2 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x^2} \, dx\right )+\frac {16}{5} \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x} \, dx+4 \int \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right ) \, dx+4 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log (x) \log \left (x^2\right )}{x} \, dx+8 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^2} \, dx+\int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \, dx+\int \exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right ) \, dx+\int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x} \, dx\\ &=-\left (2 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x^2} \, dx\right )+\frac {16}{5} \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x} \, dx+4 \int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \log \left (x^2\right ) \, dx+4 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log (x) \log \left (x^2\right )}{x} \, dx+8 \int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^2} \, dx+\int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \, dx+\int e^{x+\left (\frac {4}{5}+\frac {2}{x}+x+\log (x)\right ) \log ^2\left (x^2\right )} \log ^2\left (x^2\right ) \, dx+\int \frac {\exp \left (x+\frac {\left (2+x^2\right ) \log ^2\left (x^2\right )}{x}+\log \left (e^{4/5} x\right ) \log ^2\left (x^2\right )\right ) \log ^2\left (x^2\right )}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.05, size = 30, normalized size = 1.15 \begin {gather*} e^{x+\left (\frac {4}{5}+\frac {2}{x}+x\right ) \log ^2\left (x^2\right )} x^{\log ^2\left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 39, normalized size = 1.50 \begin {gather*} e^{\left (\frac {5 \, x \log \left (x^{2}\right )^{3} + 2 \, {\left (5 \, x^{2} + 4 \, x + 10\right )} \log \left (x^{2}\right )^{2} + 10 \, x^{2}}{10 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.67, size = 34, normalized size = 1.31 \begin {gather*} e^{\left (x \log \left (x^{2}\right )^{2} + \log \left (x^{2}\right )^{2} \log \left (x e^{\frac {4}{5}}\right ) + x + \frac {2 \, \log \left (x^{2}\right )^{2}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.26, size = 537, normalized size = 20.65
method | result | size |
risch | \(x^{-\frac {3 \pi ^{2}}{2}} x^{2 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )} x^{-\frac {\pi ^{2}}{2}} x^{-\frac {16 i \pi \,\mathrm {csgn}\left (i x^{2}\right )}{5}} x^{\frac {8 i \pi \,\mathrm {csgn}\left (i x \right )}{x}} x^{-\frac {8 i \pi \,\mathrm {csgn}\left (i x^{2}\right )}{x}} x^{4 i x \pi \,\mathrm {csgn}\left (i x \right )} x^{-4 i x \pi \,\mathrm {csgn}\left (i x^{2}\right )} x^{\frac {16 i \pi \,\mathrm {csgn}\left (i x \right )}{5}} {\mathrm e}^{\frac {-5 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6} x^{2}+20 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right ) x^{2}-30 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2} x^{2}+20 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3} x^{2}-5 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4} x^{2}-4 x \,\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}+16 x \,\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right )-24 x \,\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}+16 x \,\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3}-4 x \,\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4}-10 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}+40 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right )-60 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}+40 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3}-10 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4}-40 i x \ln \relax (x )^{2} \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}-40 i x \ln \relax (x )^{2} \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+80 i x \ln \relax (x )^{2} \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )+80 x \ln \relax (x )^{3}+80 x^{2} \ln \relax (x )^{2}+64 x \ln \relax (x )^{2}+160 \ln \relax (x )^{2}+20 x^{2}}{20 x}}\) | \(537\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 31, normalized size = 1.19 \begin {gather*} e^{\left (4 \, x \log \relax (x)^{2} + 4 \, \log \relax (x)^{3} + \frac {16}{5} \, \log \relax (x)^{2} + x + \frac {8 \, \log \relax (x)^{2}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.72, size = 41, normalized size = 1.58 \begin {gather*} x^{{\ln \left (x^2\right )}^2}\,{\mathrm {e}}^{\frac {2\,{\ln \left (x^2\right )}^2}{x}}\,{\mathrm {e}}^{\frac {4\,{\ln \left (x^2\right )}^2}{5}}\,{\mathrm {e}}^x\,{\mathrm {e}}^{x\,{\ln \left (x^2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.44, size = 36, normalized size = 1.38 \begin {gather*} e^{\frac {x^{2} + x \left (\frac {\log {\left (x^{2} \right )}}{2} + \frac {4}{5}\right ) \log {\left (x^{2} \right )}^{2} + \left (x^{2} + 2\right ) \log {\left (x^{2} \right )}^{2}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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