Optimal. Leaf size=22 \[ \frac {16 \left (-3+x+x^2-\frac {x}{4 \log (2)}\right )}{9 x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.18, number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {12, 186, 37} \begin {gather*} -\frac {(x (1-4 \log (2))+24 \log (2))^2}{108 x^2 \log ^2(2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 37
Rule 186
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {4 x+(96-16 x) \log (2)}{x^3} \, dx}{9 \log (2)}\\ &=\frac {\int \frac {4 x (1-4 \log (2))+96 \log (2)}{x^3} \, dx}{9 \log (2)}\\ &=-\frac {(x (1-4 \log (2))+24 \log (2))^2}{108 x^2 \log ^2(2)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \begin {gather*} \frac {4 (-12 \log (2)+x (-1+\log (16)))}{9 x^2 \log (2)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 20, normalized size = 0.91 \begin {gather*} \frac {4 \, {\left (4 \, {\left (x - 3\right )} \log \relax (2) - x\right )}}{9 \, x^{2} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 22, normalized size = 1.00 \begin {gather*} \frac {4 \, {\left (4 \, x \log \relax (2) - x - 12 \, \log \relax (2)\right )}}{9 \, x^{2} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 20, normalized size = 0.91
method | result | size |
norman | \(\frac {-\frac {16}{3}+\frac {4 \left (4 \ln \relax (2)-1\right ) x}{9 \ln \relax (2)}}{x^{2}}\) | \(20\) |
gosper | \(\frac {\frac {16 x \ln \relax (2)}{9}-\frac {16 \ln \relax (2)}{3}-\frac {4 x}{9}}{x^{2} \ln \relax (2)}\) | \(23\) |
risch | \(\frac {\left (16 \ln \relax (2)-4\right ) x -48 \ln \relax (2)}{9 \ln \relax (2) x^{2}}\) | \(23\) |
default | \(\frac {-\frac {48 \ln \relax (2)}{x^{2}}-\frac {4 \left (-4 \ln \relax (2)+1\right )}{x}}{9 \ln \relax (2)}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.76, size = 22, normalized size = 1.00 \begin {gather*} \frac {4 \, {\left (x {\left (4 \, \log \relax (2) - 1\right )} - 12 \, \log \relax (2)\right )}}{9 \, x^{2} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.43, size = 23, normalized size = 1.05 \begin {gather*} -\frac {48\,\ln \relax (2)-x\,\left (16\,\ln \relax (2)-4\right )}{9\,x^2\,\ln \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 20, normalized size = 0.91 \begin {gather*} \frac {x \left (-4 + 16 \log {\relax (2 )}\right ) - 48 \log {\relax (2 )}}{9 x^{2} \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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