Optimal. Leaf size=20 \[ \log \left (x+x \left (x+5 \left (\frac {1}{x}+16 x^2\right )^2\right )\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 21, normalized size of antiderivative = 1.05, number of steps used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {2074, 1587} \begin {gather*} \log \left (1280 x^6+161 x^3+x^2+5\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{x}+\frac {x \left (2+483 x+7680 x^4\right )}{5+x^2+161 x^3+1280 x^6}\right ) \, dx\\ &=-\log (x)+\int \frac {x \left (2+483 x+7680 x^4\right )}{5+x^2+161 x^3+1280 x^6} \, dx\\ &=-\log (x)+\log \left (5+x^2+161 x^3+1280 x^6\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.05 \begin {gather*} -\log (x)+\log \left (5+x^2+161 x^3+1280 x^6\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 21, normalized size = 1.05 \begin {gather*} \log \left (1280 \, x^{6} + 161 \, x^{3} + x^{2} + 5\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 22, normalized size = 1.10 \begin {gather*} \log \left (1280 \, x^{6} + 161 \, x^{3} + x^{2} + 5\right ) - \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 = 22, normalized size = 1.10
method | result | size |
default | \(-\ln \relax (x )+\ln \left (1280 x^{6}+161 x^{3}+x^{2}+5\right )\) | \(22\) |
norman | \(-\ln \relax (x )+\ln \left (1280 x^{6}+161 x^{3}+x^{2}+5\right )\) | \(22\) |
risch | \(-\ln \relax (x )+\ln \left (1280 x^{6}+161 x^{3}+x^{2}+5\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 21, normalized size = 1.05 \begin {gather*} \log \left (1280 \, x^{6} + 161 \, x^{3} + x^{2} + 5\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 21, normalized size = 1.05 \begin {gather*} \ln \left (1280\,x^6+161\,x^3+x^2+5\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 19, normalized size = 0.95 \begin {gather*} - \log {\relax (x )} + \log {\left (1280 x^{6} + 161 x^{3} + x^{2} + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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