Optimal. Leaf size=26 \[ \frac {3}{x^2 \log \left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \]
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Rubi [F] time = 2.12, 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 {-27 x+123 x^2-30 x^3+\left (576-168 x+126 x^2-30 x^3+(120-30 x) \log (4-x)\right ) \log \left (\frac {1}{5} \left (24-x+5 x^2+5 \log (4-x)\right )\right )}{\left (-96 x^3+28 x^4-21 x^5+5 x^6+\left (-20 x^3+5 x^4\right ) \log (4-x)\right ) \log ^2\left (\frac {1}{5} \left (24-x+5 x^2+5 \log (4-x)\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (\frac {x \left (-9+41 x-10 x^2\right )}{(-4+x) \left (24-x+5 x^2+5 \log (4-x)\right )}-2 \log \left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )\right )}{x^3 \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx\\ &=3 \int \frac {\frac {x \left (-9+41 x-10 x^2\right )}{(-4+x) \left (24-x+5 x^2+5 \log (4-x)\right )}-2 \log \left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )}{x^3 \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx\\ &=3 \int \left (\frac {-9+41 x-10 x^2}{(-4+x) x^2 \left (24-x+5 x^2+5 \log (4-x)\right ) \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )}-\frac {2}{x^3 \log \left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )}\right ) \, dx\\ &=3 \int \frac {-9+41 x-10 x^2}{(-4+x) x^2 \left (24-x+5 x^2+5 \log (4-x)\right ) \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx-6 \int \frac {1}{x^3 \log \left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx\\ &=3 \int \left (-\frac {5}{16 (-4+x) \left (24-x+5 x^2+5 \log (4-x)\right ) \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )}+\frac {9}{4 x^2 \left (24-x+5 x^2+5 \log (4-x)\right ) \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )}-\frac {155}{16 x \left (24-x+5 x^2+5 \log (4-x)\right ) \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )}\right ) \, dx-6 \int \frac {1}{x^3 \log \left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx\\ &=-\left (\frac {15}{16} \int \frac {1}{(-4+x) \left (24-x+5 x^2+5 \log (4-x)\right ) \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx\right )-6 \int \frac {1}{x^3 \log \left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx+\frac {27}{4} \int \frac {1}{x^2 \left (24-x+5 x^2+5 \log (4-x)\right ) \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx-\frac {465}{16} \int \frac {1}{x \left (24-x+5 x^2+5 \log (4-x)\right ) \log ^2\left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 26, normalized size = 1.00 \begin {gather*} \frac {3}{x^2 \log \left (\frac {24}{5}-\frac {x}{5}+x^2+\log (4-x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 22, normalized size = 0.85 \begin {gather*} \frac {3}{x^{2} \log \left (x^{2} - \frac {1}{5} \, x + \log \left (-x + 4\right ) + \frac {24}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 35, normalized size = 1.35 \begin {gather*} -\frac {3}{x^{2} \log \relax (5) - x^{2} \log \left (5 \, x^{2} - x + 5 \, \log \left (-x + 4\right ) + 24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 0.88
method | result | size |
risch | \(\frac {3}{\ln \left (\ln \left (-x +4\right )+x^{2}-\frac {x}{5}+\frac {24}{5}\right ) x^{2}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 35, normalized size = 1.35 \begin {gather*} -\frac {3}{x^{2} \log \relax (5) - x^{2} \log \left (5 \, x^{2} - x + 5 \, \log \left (-x + 4\right ) + 24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.52, size = 22, normalized size = 0.85 \begin {gather*} \frac {3}{x^2\,\ln \left (\ln \left (4-x\right )-\frac {x}{5}+x^2+\frac {24}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.43, size = 20, normalized size = 0.77 \begin {gather*} \frac {3}{x^{2} \log {\left (x^{2} - \frac {x}{5} + \log {\left (4 - x \right )} + \frac {24}{5} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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