Optimal. Leaf size=21 \[ x \left (\frac {57122 (4-x)^4 \log ^2(2)}{x^2}+\log (5)\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.86, number of steps used = 2, number of rules used = 1, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {14} \begin {gather*} 57122 x^3 \log ^2(2)-913952 x^2 \log ^2(2)+x \left (5483712 \log ^2(2)+\log (5)\right )+\frac {14623232 \log ^2(2)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {14623232 \log ^2(2)}{x^2}-1827904 x \log ^2(2)+171366 x^2 \log ^2(2)+5483712 \log ^2(2) \left (1+\frac {\log (5)}{5483712 \log ^2(2)}\right )\right ) \, dx\\ &=\frac {14623232 \log ^2(2)}{x}-913952 x^2 \log ^2(2)+57122 x^3 \log ^2(2)+x \left (5483712 \log ^2(2)+\log (5)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 39, normalized size = 1.86 \begin {gather*} \frac {14623232 \log ^2(2)}{x}+5483712 x \log ^2(2)-913952 x^2 \log ^2(2)+57122 x^3 \log ^2(2)+x \log (5) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 32, normalized size = 1.52 \begin {gather*} \frac {x^{2} \log \relax (5) + 57122 \, {\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} + 256\right )} \log \relax (2)^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.38, size = 39, normalized size = 1.86 \begin {gather*} 57122 \, x^{3} \log \relax (2)^{2} - 913952 \, x^{2} \log \relax (2)^{2} + 5483712 \, x \log \relax (2)^{2} + x \log \relax (5) + \frac {14623232 \, \log \relax (2)^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 40, normalized size = 1.90
method | result | size |
default | \(57122 x^{3} \ln \relax (2)^{2}-913952 x^{2} \ln \relax (2)^{2}+5483712 x \ln \relax (2)^{2}+x \ln \relax (5)+\frac {14623232 \ln \relax (2)^{2}}{x}\) | \(40\) |
risch | \(57122 x^{3} \ln \relax (2)^{2}-913952 x^{2} \ln \relax (2)^{2}+5483712 x \ln \relax (2)^{2}+x \ln \relax (5)+\frac {14623232 \ln \relax (2)^{2}}{x}\) | \(40\) |
norman | \(\frac {57122 x^{4} \ln \relax (2)^{2}-913952 x^{3} \ln \relax (2)^{2}+\left (5483712 \ln \relax (2)^{2}+\ln \relax (5)\right ) x^{2}+14623232 \ln \relax (2)^{2}}{x}\) | \(43\) |
gosper | \(\frac {57122 x^{4} \ln \relax (2)^{2}-913952 x^{3} \ln \relax (2)^{2}+5483712 x^{2} \ln \relax (2)^{2}+x^{2} \ln \relax (5)+14623232 \ln \relax (2)^{2}}{x}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.65, size = 39, normalized size = 1.86 \begin {gather*} 57122 \, x^{3} \log \relax (2)^{2} - 913952 \, x^{2} \log \relax (2)^{2} + {\left (5483712 \, \log \relax (2)^{2} + \log \relax (5)\right )} x + \frac {14623232 \, \log \relax (2)^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.53, size = 39, normalized size = 1.86 \begin {gather*} \frac {14623232\,{\ln \relax (2)}^2}{x}-913952\,x^2\,{\ln \relax (2)}^2+57122\,x^3\,{\ln \relax (2)}^2+x\,\left (\ln \relax (5)+5483712\,{\ln \relax (2)}^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 39, normalized size = 1.86 \begin {gather*} 57122 x^{3} \log {\relax (2 )}^{2} - 913952 x^{2} \log {\relax (2 )}^{2} + x \left (\log {\relax (5 )} + 5483712 \log {\relax (2 )}^{2}\right ) + \frac {14623232 \log {\relax (2 )}^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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