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 = 0.27, 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 = 0.10, 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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Maple [A]
time = 0.30, size = 34, normalized size = 1.31
method | result | size |
risch | \(x^{-2 \left (5+x \right ) \ln \left (2\right )^{2}} {\mathrm e}^{2+2 x \ln \left (2\right )^{2}}-x^{2}\) | \(31\) |
default | \({\mathrm e}^{2} {\mathrm e}^{2 \left (-x -5\right ) \ln \left (2\right )^{2} \ln \left (x \right )+2 x \ln \left (2\right )^{2}}-x^{2}\) | \(34\) |
norman | \({\mathrm e}^{2} {\mathrm e}^{2 \left (-x -5\right ) \ln \left (2\right )^{2} \ln \left (x \right )+2 x \ln \left (2\right )^{2}}-x^{2}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 33, normalized size = 1.27 \begin {gather*} -x^{2} + e^{\left (-2 \, x \log \left (2\right )^{2} \log \left (x\right ) + 2 \, x \log \left (2\right )^{2} - 10 \, \log \left (2\right )^{2} \log \left (x\right ) + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 27, normalized size = 1.04 \begin {gather*} -x^{2} + e^{\left (-2 \, {\left (x + 5\right )} \log \left (2\right )^{2} \log \left (x\right ) + 2 \, x \log \left (2\right )^{2} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 31, normalized size = 1.19 \begin {gather*} - x^{2} + e^{2} e^{2 x \log {\left (2 \right )}^{2} + 2 \left (- x - 5\right ) \log {\left (2 \right )}^{2} \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 33, normalized size = 1.27 \begin {gather*} -x^{2} + e^{\left (-2 \, x \log \left (2\right )^{2} \log \left (x\right ) + 2 \, x \log \left (2\right )^{2} - 10 \, \log \left (2\right )^{2} \log \left (x\right ) + 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 \left (2\right )}^2}\,{\mathrm {e}}^2}{x^{10\,{\ln \left (2\right )}^2}\,x^{2\,x\,{\ln \left (2\right )}^2}}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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