Optimal. Leaf size=26 \[ \frac {1+\frac {9-\frac {11 x}{12}}{x}+x}{\log \left (4-\log \left (\frac {5}{3}\right )\right )} \]
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Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.15, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 14}
\begin {gather*} \frac {x}{\log \left (4-\log \left (\frac {5}{3}\right )\right )}+\frac {9}{x \log \left (4-\log \left (\frac {5}{3}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-9+x^2}{x^2} \, dx}{\log \left (4-\log \left (\frac {5}{3}\right )\right )}\\ &=\frac {\int \left (1-\frac {9}{x^2}\right ) \, dx}{\log \left (4-\log \left (\frac {5}{3}\right )\right )}\\ &=\frac {9}{x \log \left (4-\log \left (\frac {5}{3}\right )\right )}+\frac {x}{\log \left (4-\log \left (\frac {5}{3}\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 0.73 \begin {gather*} \frac {\frac {9}{x}+x}{\log \left (4-\log \left (\frac {5}{3}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 16, normalized size = 0.62
method | result | size |
default | \(\frac {x +\frac {9}{x}}{\ln \left (\ln \left (\frac {3}{5}\right )+4\right )}\) | \(16\) |
gosper | \(\frac {x^{2}+9}{x \ln \left (\ln \left (\frac {3}{5}\right )+4\right )}\) | \(17\) |
norman | \(\frac {\frac {x^{2}}{\ln \left (\ln \left (\frac {3}{5}\right )+4\right )}+\frac {9}{\ln \left (\ln \left (\frac {3}{5}\right )+4\right )}}{x}\) | \(26\) |
risch | \(\frac {x}{\ln \left (\ln \left (3\right )-\ln \left (5\right )+4\right )}+\frac {9}{\ln \left (\ln \left (3\right )-\ln \left (5\right )+4\right ) x}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 15, normalized size = 0.58 \begin {gather*} \frac {x + \frac {9}{x}}{\log \left (\log \left (\frac {3}{5}\right ) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 16, normalized size = 0.62 \begin {gather*} \frac {x^{2} + 9}{x \log \left (\log \left (\frac {3}{5}\right ) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 0.54 \begin {gather*} \frac {x + \frac {9}{x}}{\log {\left (- \log {\left (5 \right )} + \log {\left (3 \right )} + 4 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 0.58 \begin {gather*} \frac {x + \frac {9}{x}}{\log \left (\log \left (\frac {3}{5}\right ) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.59, size = 16, normalized size = 0.62 \begin {gather*} \frac {x^2+9}{x\,\ln \left (\ln \left (\frac {3}{5}\right )+4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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