Optimal. Leaf size=27 \[ e^5-(5-x)^2 x^4+\log (2) \left (-x^2+\log (x)\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.04, number of steps used = 2, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {14} \begin {gather*} -x^6+10 x^5-25 x^4-x^2 \log (2)+\log (2) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-100 x^3+50 x^4-6 x^5+\frac {\log (2)}{x}-2 x \log (2)\right ) \, dx\\ &=-25 x^4+10 x^5-x^6-x^2 \log (2)+\log (2) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 1.11 \begin {gather*} -25 x^4+10 x^5-x^6-\frac {1}{2} x^2 \log (4)+\log (2) \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 28, normalized size = 1.04 \begin {gather*} -x^{6} + 10 \, x^{5} - 25 \, x^{4} - x^{2} \log \relax (2) + \log \relax (2) \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 29, normalized size = 1.07 \begin {gather*} -x^{6} + 10 \, x^{5} - 25 \, x^{4} - x^{2} \log \relax (2) + \log \relax (2) \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 29, normalized size = 1.07
method | result | size |
default | \(-x^{6}+10 x^{5}-25 x^{4}-x^{2} \ln \relax (2)+\ln \relax (2) \ln \relax (x )\) | \(29\) |
norman | \(-x^{6}+10 x^{5}-25 x^{4}-x^{2} \ln \relax (2)+\ln \relax (2) \ln \relax (x )\) | \(29\) |
risch | \(-x^{6}+10 x^{5}-25 x^{4}-x^{2} \ln \relax (2)+\ln \relax (2) \ln \relax (x )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 28, normalized size = 1.04 \begin {gather*} -x^{6} + 10 \, x^{5} - 25 \, x^{4} - x^{2} \log \relax (2) + \log \relax (2) \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 28, normalized size = 1.04 \begin {gather*} \ln \relax (2)\,\ln \relax (x)-x^2\,\ln \relax (2)-25\,x^4+10\,x^5-x^6 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 26, normalized size = 0.96 \begin {gather*} - x^{6} + 10 x^{5} - 25 x^{4} - x^{2} \log {\relax (2 )} + \log {\relax (2 )} \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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