Optimal. Leaf size=23 \[ \log \left (x (1+(5+3 x) (2 x-\log (2 x)))^2\right ) \]
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Rubi [F]
time = 0.56, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {9-24 x-30 x^2+(5+9 x) \log (2 x)}{-x-10 x^2-6 x^3+\left (5 x+3 x^2\right ) \log (2 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {5+9 x}{x (5+3 x)}+\frac {2 \left (-25+17 x+51 x^2+18 x^3\right )}{x (5+3 x) \left (1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)\right )}\right ) \, dx\\ &=2 \int \frac {-25+17 x+51 x^2+18 x^3}{x (5+3 x) \left (1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)\right )} \, dx+\int \frac {5+9 x}{x (5+3 x)} \, dx\\ &=2 \int \left (\frac {7}{1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)}-\frac {5}{x \left (1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)\right )}+\frac {6 x}{1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)}-\frac {3}{(5+3 x) \left (1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)\right )}\right ) \, dx+\int \left (\frac {1}{x}+\frac {6}{5+3 x}\right ) \, dx\\ &=\log (x)+2 \log (5+3 x)-6 \int \frac {1}{(5+3 x) \left (1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)\right )} \, dx-10 \int \frac {1}{x \left (1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)\right )} \, dx+12 \int \frac {x}{1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)} \, dx+14 \int \frac {1}{1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 29, normalized size = 1.26 \begin {gather*} \log (x)+2 \log \left (1+10 x+6 x^2-5 \log (2 x)-3 x \log (2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.50, size = 32, normalized size = 1.39
method | result | size |
derivativedivides | \(\ln \left (2 x \right )+2 \ln \left (6 x \ln \left (2 x \right )-12 x^{2}+10 \ln \left (2 x \right )-20 x -2\right )\) | \(32\) |
default | \(\ln \left (2 x \right )+2 \ln \left (6 x \ln \left (2 x \right )-12 x^{2}+10 \ln \left (2 x \right )-20 x -2\right )\) | \(32\) |
norman | \(\ln \left (2 x \right )+2 \ln \left (6 x^{2}-3 x \ln \left (2 x \right )+10 x -5 \ln \left (2 x \right )+1\right )\) | \(32\) |
risch | \(\ln \left (x \right )+2 \ln \left (3 x +5\right )+2 \ln \left (\ln \left (2 x \right )-\frac {6 x^{2}+10 x +1}{3 x +5}\right )\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 52 vs.
\(2 (23) = 46\).
time = 0.50, size = 52, normalized size = 2.26 \begin {gather*} 2 \, \log \left (3 \, x + 5\right ) + \log \left (x\right ) + 2 \, \log \left (-\frac {6 \, x^{2} - x {\left (3 \, \log \left (2\right ) - 10\right )} - {\left (3 \, x + 5\right )} \log \left (x\right ) - 5 \, \log \left (2\right ) + 1}{3 \, x + 5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.45, size = 44, normalized size = 1.91 \begin {gather*} 2 \, \log \left (3 \, x + 5\right ) + \log \left (x\right ) + 2 \, \log \left (-\frac {6 \, x^{2} - {\left (3 \, x + 5\right )} \log \left (2 \, x\right ) + 10 \, x + 1}{3 \, x + 5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.22, size = 36, normalized size = 1.57 \begin {gather*} \log {\left (x \right )} + 2 \log {\left (x + \frac {5}{3} \right )} + 2 \log {\left (\log {\left (2 x \right )} + \frac {- 6 x^{2} - 10 x - 1}{3 x + 5} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 29, normalized size = 1.26 \begin {gather*} 2 \, \log \left (-6 \, x^{2} + 3 \, x \log \left (2 \, x\right ) - 10 \, x + 5 \, \log \left (2 \, x\right ) - 1\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.95, size = 29, normalized size = 1.26 \begin {gather*} 2\,\ln \left (10\,x-5\,\ln \left (2\,x\right )-3\,x\,\ln \left (2\,x\right )+6\,x^2+1\right )+\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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