Optimal. Leaf size=20 \[ \left (2-x+x \left (16 e^4+x\right )\right ) \log (5+\log (16)) \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.05, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {9} \begin {gather*} \frac {1}{4} \left (-2 x-16 e^4+1\right )^2 \log (5+\log (16)) \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \left (1-16 e^4-2 x\right )^2 \log (5+\log (16))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 0.95 \begin {gather*} \left (-x+16 e^4 x+x^2\right ) \log (5+\log (16)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 20, normalized size = 1.00 \begin {gather*} {\left (x^{2} + 16 \, x e^{4} - x\right )} \log \left (4 \, \log \relax (2) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 20, normalized size = 1.00 \begin {gather*} {\left (x^{2} + 16 \, x e^{4} - x\right )} \log \left (4 \, \log \relax (2) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.85
method | result | size |
gosper | \(x \left (x +16 \,{\mathrm e}^{4}-1\right ) \ln \left (4 \ln \relax (2)+5\right )\) | \(17\) |
default | \(\ln \left (4 \ln \relax (2)+5\right ) \left (16 x \,{\mathrm e}^{4}+x^{2}-x \right )\) | \(21\) |
risch | \(16 \ln \left (4 \ln \relax (2)+5\right ) x \,{\mathrm e}^{4}+\ln \left (4 \ln \relax (2)+5\right ) x^{2}-\ln \left (4 \ln \relax (2)+5\right ) x\) | \(35\) |
norman | \(\left (16 \ln \left (4 \ln \relax (2)+5\right ) {\mathrm e}^{4}-\ln \left (4 \ln \relax (2)+5\right )\right ) x +\ln \left (4 \ln \relax (2)+5\right ) x^{2}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 20, normalized size = 1.00 \begin {gather*} {\left (x^{2} + 16 \, x e^{4} - x\right )} \log \left (4 \, \log \relax (2) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 18, normalized size = 0.90 \begin {gather*} \frac {\ln \left (\ln \left (16\right )+5\right )\,{\left (2\,x+16\,{\mathrm {e}}^4-1\right )}^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 34, normalized size = 1.70 \begin {gather*} x^{2} \log {\left (4 \log {\relax (2 )} + 5 \right )} + x \left (- \log {\left (4 \log {\relax (2 )} + 5 \right )} + 16 e^{4} \log {\left (4 \log {\relax (2 )} + 5 \right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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