Optimal. Leaf size=22 \[ 8+e^{10+2 x-x^2 \log \left (\log ^2(x)\right )}-x \]
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Rubi [A] time = 0.33, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6742, 2288} \begin {gather*} e^{2 x+10} \log ^2(x)^{-x^2}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1-\frac {2 e^{10+2 x} \log ^2(x)^{-x^2} \left (x-\log (x)+x \log (x) \log \left (\log ^2(x)\right )\right )}{\log (x)}\right ) \, dx\\ &=-x-2 \int \frac {e^{10+2 x} \log ^2(x)^{-x^2} \left (x-\log (x)+x \log (x) \log \left (\log ^2(x)\right )\right )}{\log (x)} \, dx\\ &=-x+e^{10+2 x} \log ^2(x)^{-x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.21, size = 22, normalized size = 1.00 \begin {gather*} -x+e^{10+2 x} \log ^2(x)^{-x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 20, normalized size = 0.91 \begin {gather*} -x + e^{\left (-x^{2} \log \left (\log \relax (x)^{2}\right ) + 2 \, x + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.44, size = 86, normalized size = 3.91
method | result | size |
risch | \(-x +\ln \relax (x )^{-2 x^{2}} {\mathrm e}^{2 x +10} {\mathrm e}^{\frac {i x^{2} \pi \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{3}}{2}} {\mathrm e}^{-i x^{2} \pi \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )} {\mathrm e}^{\frac {i x^{2} \pi \,\mathrm {csgn}\left (i \ln \relax (x )^{2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right )^{2}}{2}}\) | \(86\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.00, size = 18, normalized size = 0.82 \begin {gather*} -x + e^{\left (-2 \, x^{2} \log \left (\log \relax (x)\right ) + 2 \, x + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.03, size = 21, normalized size = 0.95 \begin {gather*} \frac {{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{10}}{{\left ({\ln \relax (x)}^2\right )}^{x^2}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.47, size = 17, normalized size = 0.77 \begin {gather*} - x + e^{- x^{2} \log {\left (\log {\relax (x )}^{2} \right )} + 2 x + 10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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