Optimal. Leaf size=28 \[ 2+\frac {3 \left (1-x^2+\left (-4+\frac {2}{3} (-x+\log (4))\right )^2\right )}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 14} \begin {gather*} \frac {153+4 \log ^2(4)-48 \log (4)}{3 x}-\frac {5 x}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {-153-5 x^2+48 \log (4)-4 \log ^2(4)}{x^2} \, dx\\ &=\frac {1}{3} \int \left (-5+\frac {-153+48 \log (4)-4 \log ^2(4)}{x^2}\right ) \, dx\\ &=-\frac {5 x}{3}+\frac {153-48 \log (4)+4 \log ^2(4)}{3 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 0.89 \begin {gather*} \frac {1}{3} \left (-5 x-\frac {-153+48 \log (4)-4 \log ^2(4)}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 22, normalized size = 0.79 \begin {gather*} -\frac {5 \, x^{2} - 16 \, \log \relax (2)^{2} + 96 \, \log \relax (2) - 153}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 21, normalized size = 0.75 \begin {gather*} -\frac {5}{3} \, x + \frac {16 \, \log \relax (2)^{2} - 96 \, \log \relax (2) + 153}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 22, normalized size = 0.79
method | result | size |
default | \(-\frac {5 x}{3}-\frac {-16 \ln \relax (2)^{2}+96 \ln \relax (2)-153}{3 x}\) | \(22\) |
norman | \(\frac {-\frac {5 x^{2}}{3}+\frac {16 \ln \relax (2)^{2}}{3}-32 \ln \relax (2)+51}{x}\) | \(22\) |
gosper | \(\frac {16 \ln \relax (2)^{2}-5 x^{2}-96 \ln \relax (2)+153}{3 x}\) | \(23\) |
risch | \(-\frac {5 x}{3}+\frac {16 \ln \relax (2)^{2}}{3 x}-\frac {32 \ln \relax (2)}{x}+\frac {51}{x}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 21, normalized size = 0.75 \begin {gather*} -\frac {5}{3} \, x + \frac {16 \, \log \relax (2)^{2} - 96 \, \log \relax (2) + 153}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 20, normalized size = 0.71 \begin {gather*} \frac {\frac {16\,{\ln \relax (2)}^2}{3}-32\,\ln \relax (2)+51}{x}-\frac {5\,x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 22, normalized size = 0.79 \begin {gather*} - \frac {5 x}{3} - \frac {-153 - 16 \log {\relax (2 )}^{2} + 96 \log {\relax (2 )}}{3 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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