Optimal. Leaf size=26 \[ 2+e^{2+2 \log ^2(2) (x-(5+x) \log (x))}-x^2 \]
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Rubi [F] time = 0.41, 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 {-2 x^2+e^{2 x \log ^2(2)+2 (-5-x) \log ^2(2) \log (x)} \left (-10 e^2 \log ^2(2)-2 e^2 x \log ^2(2) \log (x)\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 x+2 e^{2+2 x \log ^2(2)} x^{-1-10 \log ^2(2)-2 x \log ^2(2)} \log ^2(2) (-5-x \log (x))\right ) \, dx\\ &=-x^2+\left (2 \log ^2(2)\right ) \int e^{2+2 x \log ^2(2)} x^{-1-10 \log ^2(2)-2 x \log ^2(2)} (-5-x \log (x)) \, dx\\ &=-x^2+\left (2 \log ^2(2)\right ) \int \left (-5 e^{2+2 x \log ^2(2)} x^{-1-10 \log ^2(2)-2 x \log ^2(2)}-e^{2+2 x \log ^2(2)} x^{-10 \log ^2(2)-2 x \log ^2(2)} \log (x)\right ) \, dx\\ &=-x^2-\left (2 \log ^2(2)\right ) \int e^{2+2 x \log ^2(2)} x^{-10 \log ^2(2)-2 x \log ^2(2)} \log (x) \, dx-\left (10 \log ^2(2)\right ) \int e^{2+2 x \log ^2(2)} x^{-1-10 \log ^2(2)-2 x \log ^2(2)} \, dx\\ &=-x^2+\left (2 \log ^2(2)\right ) \int \frac {\int e^{2+2 x \log ^2(2)} x^{-10 \log ^2(2)-2 x \log ^2(2)} \, dx}{x} \, dx-\left (10 \log ^2(2)\right ) \int e^{2+2 x \log ^2(2)} x^{-1-10 \log ^2(2)-2 x \log ^2(2)} \, dx-\left (2 \log ^2(2) \log (x)\right ) \int e^{2+2 x \log ^2(2)} x^{-10 \log ^2(2)-2 x \log ^2(2)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.21, size = 29, normalized size = 1.12 \begin {gather*} -x^2+e^{2+2 x \log ^2(2)} x^{-2 (5+x) \log ^2(2)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 27, normalized size = 1.04 \begin {gather*} -x^{2} + e^{\left (-2 \, {\left (x + 5\right )} \log \relax (2)^{2} \log \relax (x) + 2 \, x \log \relax (2)^{2} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 33, normalized size = 1.27 \begin {gather*} -x^{2} + e^{\left (-2 \, x \log \relax (2)^{2} \log \relax (x) + 2 \, x \log \relax (2)^{2} - 10 \, \log \relax (2)^{2} \log \relax (x) + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.24, size = 31, normalized size = 1.19
method | result | size |
risch | \(x^{-2 \left (5+x \right ) \ln \relax (2)^{2}} {\mathrm e}^{2+2 x \ln \relax (2)^{2}}-x^{2}\) | \(31\) |
default | \({\mathrm e}^{2} {\mathrm e}^{\left (-2 x -10\right ) \ln \relax (2)^{2} \ln \relax (x )+2 x \ln \relax (2)^{2}}-x^{2}\) | \(34\) |
norman | \({\mathrm e}^{2} {\mathrm e}^{\left (-2 x -10\right ) \ln \relax (2)^{2} \ln \relax (x )+2 x \ln \relax (2)^{2}}-x^{2}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 33, normalized size = 1.27 \begin {gather*} -x^{2} + e^{\left (-2 \, x \log \relax (2)^{2} \log \relax (x) + 2 \, x \log \relax (2)^{2} - 10 \, \log \relax (2)^{2} \log \relax (x) + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.49, size = 38, normalized size = 1.46 \begin {gather*} \frac {{\mathrm {e}}^{2\,x\,{\ln \relax (2)}^2}\,{\mathrm {e}}^2}{x^{10\,{\ln \relax (2)}^2}\,x^{2\,x\,{\ln \relax (2)}^2}}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 31, normalized size = 1.19 \begin {gather*} - x^{2} + e^{2} e^{2 x \log {\relax (2 )}^{2} + 2 \left (- x - 5\right ) \log {\relax (2 )}^{2} \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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