Optimal. Leaf size=25 \[ -\frac {\left (-4+\frac {1}{\log (3)}\right )^2}{x^2}+\frac {\log (x)}{\log (4-x)} \]
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Rubi [F]
time = 0.31, 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 {\left (-4 x^2+x^3\right ) \log ^2(3) \log (4-x)+\left (-8+2 x+(64-16 x) \log (3)+(-128+32 x) \log ^2(3)\right ) \log ^2(4-x)-x^3 \log ^2(3) \log (x)}{\left (-4 x^3+x^4\right ) \log ^2(3) \log ^2(4-x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {\left (-4 x^2+x^3\right ) \log ^2(3) \log (4-x)+\left (-8+2 x+(64-16 x) \log (3)+(-128+32 x) \log ^2(3)\right ) \log ^2(4-x)-x^3 \log ^2(3) \log (x)}{\left (-4 x^3+x^4\right ) \log ^2(4-x)} \, dx}{\log ^2(3)}\\ &=\frac {\int \frac {\left (-4 x^2+x^3\right ) \log ^2(3) \log (4-x)+\left (-8+2 x+(64-16 x) \log (3)+(-128+32 x) \log ^2(3)\right ) \log ^2(4-x)-x^3 \log ^2(3) \log (x)}{(-4+x) x^3 \log ^2(4-x)} \, dx}{\log ^2(3)}\\ &=\frac {\int \left (\frac {2 (-1+\log (81))^2}{x^3}+\frac {\log ^2(3)}{x \log (4-x)}-\frac {\log ^2(3) \log (x)}{(-4+x) \log ^2(4-x)}\right ) \, dx}{\log ^2(3)}\\ &=-\frac {(1-\log (81))^2}{x^2 \log ^2(3)}+\int \frac {1}{x \log (4-x)} \, dx-\int \frac {\log (x)}{(-4+x) \log ^2(4-x)} \, dx\\ &=-\frac {(1-\log (81))^2}{x^2 \log ^2(3)}+\int \frac {1}{x \log (4-x)} \, dx-\text {Subst}\left (\int \frac {\log (4-x)}{x \log ^2(x)} \, dx,x,4-x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.13, size = 27, normalized size = 1.08 \begin {gather*} -\frac {(-1+\log (81))^2}{x^2 \log ^2(3)}+\frac {\log (x)}{\log (4-x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.37, size = 36, normalized size = 1.44
method | result | size |
risch | \(-\frac {16}{x^{2}}+\frac {8}{\ln \left (3\right ) x^{2}}-\frac {1}{\ln \left (3\right )^{2} x^{2}}+\frac {\ln \left (x \right )}{\ln \left (-x +4\right )}\) | \(36\) |
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. 117 vs.
\(2 (25) = 50\).
time = 0.61, size = 117, normalized size = 4.68 \begin {gather*} -\frac {4 \, {\left (\frac {4 \, {\left (x + 2\right )}}{x^{2}} + \log \left (x - 4\right ) - \log \left (x\right )\right )} \log \left (3\right )^{2} - 4 \, {\left (\frac {4}{x} + \log \left (x - 4\right ) - \log \left (x\right )\right )} \log \left (3\right )^{2} - 2 \, {\left (\frac {4 \, {\left (x + 2\right )}}{x^{2}} + \log \left (x - 4\right ) - \log \left (x\right )\right )} \log \left (3\right ) + 2 \, {\left (\frac {4}{x} + \log \left (x - 4\right ) - \log \left (x\right )\right )} \log \left (3\right ) - \frac {2 \, \log \left (3\right )^{2} \log \left (x\right )}{\log \left (-x + 4\right )} + \frac {x + 2}{x^{2}} - \frac {1}{x}}{2 \, \log \left (3\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 47, normalized size = 1.88 \begin {gather*} \frac {x^{2} \log \left (3\right )^{2} \log \left (x\right ) - {\left (16 \, \log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 1\right )} \log \left (-x + 4\right )}{x^{2} \log \left (3\right )^{2} \log \left (-x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 31, normalized size = 1.24 \begin {gather*} \frac {\log {\left (x \right )}}{\log {\left (4 - x \right )}} - \frac {- 16 \log {\left (3 \right )} + 2 + 32 \log {\left (3 \right )}^{2}}{2 x^{2} \log {\left (3 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 38, normalized size = 1.52 \begin {gather*} \frac {\frac {\log \left (3\right )^{2} \log \left (x\right )}{\log \left (-x + 4\right )} - \frac {16 \, \log \left (3\right )^{2} - 8 \, \log \left (3\right ) + 1}{x^{2}}}{\log \left (3\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.74, size = 55, normalized size = 2.20 \begin {gather*} \frac {\ln \left (x\right )-\frac {\ln \left (4-x\right )\,\left (x-4\right )}{x}}{\ln \left (4-x\right )}-\frac {4\,x\,{\ln \left (3\right )}^2-8\,\ln \left (3\right )+16\,{\ln \left (3\right )}^2+1}{x^2\,{\ln \left (3\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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