Optimal. Leaf size=24 \[ 2-\frac {(2-3 x)^2}{4 x^2}+\frac {x}{-256+\log (3)} \]
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Rubi [A] time = 0.02, antiderivative size = 38, normalized size of antiderivative = 1.58, number of steps used = 4, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {6, 12, 14} \begin {gather*} -\frac {512-\log (9)}{2 x^2 (256-\log (3))}+\frac {3}{x}-\frac {x}{256-\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-512+768 x+x^3+(2-3 x) \log (3)}{x^3 (-256+\log (3))} \, dx\\ &=\frac {\int \frac {-512+768 x+x^3+(2-3 x) \log (3)}{x^3} \, dx}{-256+\log (3)}\\ &=\frac {\int \left (1-\frac {3 (-256+\log (3))}{x^2}+\frac {-512+\log (9)}{x^3}\right ) \, dx}{-256+\log (3)}\\ &=\frac {3}{x}-\frac {x}{256-\log (3)}-\frac {512-\log (9)}{2 x^2 (256-\log (3))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 1.08 \begin {gather*} \frac {256+x^3+3 x (-256+\log (3))-\log (3)}{x^2 (-256+\log (3))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 31, normalized size = 1.29 \begin {gather*} \frac {x^{3} + {\left (3 \, x - 1\right )} \log \relax (3) - 768 \, x + 256}{x^{2} \log \relax (3) - 256 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 18, normalized size = 0.75 \begin {gather*} \frac {x}{\log \relax (3) - 256} + \frac {3 \, x - 1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 0.83
method | result | size |
norman | \(\frac {-1+\frac {x^{3}}{\ln \relax (3)-256}+3 x}{x^{2}}\) | \(20\) |
gosper | \(\frac {x^{3}+3 x \ln \relax (3)-\ln \relax (3)-768 x +256}{x^{2} \left (\ln \relax (3)-256\right )}\) | \(28\) |
default | \(\frac {x -\frac {-3 \ln \relax (3)+768}{x}-\frac {2 \ln \relax (3)-512}{2 x^{2}}}{\ln \relax (3)-256}\) | \(32\) |
risch | \(\frac {x}{\ln \relax (3)-256}+\frac {\left (3 \ln \relax (3)^{2}-1536 \ln \relax (3)+196608\right ) x -\ln \relax (3)^{2}+512 \ln \relax (3)-65536}{\left (\ln \relax (3)-256\right )^{2} x^{2}}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 18, normalized size = 0.75 \begin {gather*} \frac {x}{\log \relax (3) - 256} + \frac {3 \, x - 1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 31, normalized size = 1.29 \begin {gather*} \frac {x}{\ln \relax (3)-256}+\frac {x\,\left (\ln \left (27\right )-768\right )-\ln \relax (3)+256}{x^2\,\left (\ln \relax (3)-256\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 22, normalized size = 0.92 \begin {gather*} \frac {x + \frac {x \left (-768 + 3 \log {\relax (3 )}\right ) - \log {\relax (3 )} + 256}{x^{2}}}{-256 + \log {\relax (3 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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