Optimal. Leaf size=19 \[ -5+\frac {-3+x}{x}+\frac {1}{4} (x+x \log (3)) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps used = 4, number of rules used = 3, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {6, 12, 14} \begin {gather*} \frac {1}{4} x (1+\log (3))-\frac {3}{x} \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 {12+x^2 (1+\log (3))}{4 x^2} \, dx\\ &=\frac {1}{4} \int \frac {12+x^2 (1+\log (3))}{x^2} \, dx\\ &=\frac {1}{4} \int \left (1+\frac {12}{x^2}+\log (3)\right ) \, dx\\ &=-\frac {3}{x}+\frac {1}{4} x (1+\log (3))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{4} \left (-\frac {12}{x}+x+x \log (3)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 16, normalized size = 0.84 \begin {gather*} \frac {x^{2} \log \relax (3) + x^{2} - 12}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{4} \, x \log \relax (3) + \frac {1}{4} \, x - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 15, normalized size = 0.79
method | result | size |
default | \(\frac {x \ln \relax (3)}{4}+\frac {x}{4}-\frac {3}{x}\) | \(15\) |
risch | \(\frac {x \ln \relax (3)}{4}+\frac {x}{4}-\frac {3}{x}\) | \(15\) |
gosper | \(\frac {x^{2} \ln \relax (3)+x^{2}-12}{4 x}\) | \(17\) |
norman | \(\frac {-3+\left (\frac {\ln \relax (3)}{4}+\frac {1}{4}\right ) x^{2}}{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 13, normalized size = 0.68 \begin {gather*} \frac {1}{4} \, x {\left (\log \relax (3) + 1\right )} - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 14, normalized size = 0.74 \begin {gather*} x\,\left (\frac {\ln \relax (3)}{4}+\frac {1}{4}\right )-\frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 10, normalized size = 0.53 \begin {gather*} \frac {x \left (1 + \log {\relax (3 )}\right )}{4} - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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