Optimal. Leaf size=20 \[ \frac {16}{(x+\log (3) (3+(5-\log (3)) \log (x)))^2} \]
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Rubi [A]
time = 0.31, antiderivative size = 19, normalized size of antiderivative = 0.95, number of steps
used = 3, number of rules used = 3, integrand size = 177, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6820, 12,
6818} \begin {gather*} \frac {16}{(x+(5-\log (3)) \log (3) \log (x)+\log (27))^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32 (-x+(-5+\log (3)) \log (3))}{x (x+\log (27)-(-5+\log (3)) \log (3) \log (x))^3} \, dx\\ &=32 \int \frac {-x+(-5+\log (3)) \log (3)}{x (x+\log (27)-(-5+\log (3)) \log (3) \log (x))^3} \, dx\\ &=\frac {16}{(x+\log (27)+(5-\log (3)) \log (3) \log (x))^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 0.90 \begin {gather*} \frac {16}{(x+\log (27)-(-5+\log (3)) \log (3) \log (x))^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.70, size = 26, normalized size = 1.30
method | result | size |
default | \(\frac {16}{\left (\ln \left (3\right )^{2} \ln \left (x \right )-5 \ln \left (3\right ) \ln \left (x \right )-3 \ln \left (3\right )-x \right )^{2}}\) | \(26\) |
norman | \(\frac {16}{\left (\ln \left (3\right )^{2} \ln \left (x \right )-5 \ln \left (3\right ) \ln \left (x \right )-3 \ln \left (3\right )-x \right )^{2}}\) | \(26\) |
risch | \(\frac {16}{\left (\ln \left (3\right )^{2} \ln \left (x \right )-5 \ln \left (3\right ) \ln \left (x \right )-3 \ln \left (3\right )-x \right )^{2}}\) | \(26\) |
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. 69 vs.
\(2 (20) = 40\).
time = 0.50, size = 69, normalized size = 3.45 \begin {gather*} \frac {16}{{\left (\log \left (3\right )^{4} - 10 \, \log \left (3\right )^{3} + 25 \, \log \left (3\right )^{2}\right )} \log \left (x\right )^{2} + x^{2} + 6 \, x \log \left (3\right ) + 9 \, \log \left (3\right )^{2} - 2 \, {\left (3 \, \log \left (3\right )^{3} + {\left (\log \left (3\right )^{2} - 5 \, \log \left (3\right )\right )} x - 15 \, \log \left (3\right )^{2}\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 65 vs.
\(2 (20) = 40\).
time = 0.39, size = 65, normalized size = 3.25 \begin {gather*} \frac {16}{{\left (\log \left (3\right )^{4} - 10 \, \log \left (3\right )^{3} + 25 \, \log \left (3\right )^{2}\right )} \log \left (x\right )^{2} + x^{2} + 6 \, x \log \left (3\right ) + 9 \, \log \left (3\right )^{2} - 2 \, {\left ({\left (x - 15\right )} \log \left (3\right )^{2} + 3 \, \log \left (3\right )^{3} - 5 \, x \log \left (3\right )\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 73 vs.
\(2 (17) = 34\).
time = 0.20, size = 73, normalized size = 3.65 \begin {gather*} \frac {16}{x^{2} + 6 x \log {\left (3 \right )} + \left (- 2 x \log {\left (3 \right )}^{2} + 10 x \log {\left (3 \right )} - 6 \log {\left (3 \right )}^{3} + 30 \log {\left (3 \right )}^{2}\right ) \log {\left (x \right )} + \left (- 10 \log {\left (3 \right )}^{3} + \log {\left (3 \right )}^{4} + 25 \log {\left (3 \right )}^{2}\right ) \log {\left (x \right )}^{2} + 9 \log {\left (3 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 206 vs.
\(2 (20) = 40\).
time = 0.44, size = 206, normalized size = 10.30 \begin {gather*} \frac {16 \, {\left (\log \left (3\right )^{2} - x - 5 \, \log \left (3\right )\right )}}{\log \left (3\right )^{6} \log \left (x\right )^{2} - x \log \left (3\right )^{4} \log \left (x\right )^{2} - 15 \, \log \left (3\right )^{5} \log \left (x\right )^{2} - 2 \, x \log \left (3\right )^{4} \log \left (x\right ) - 6 \, \log \left (3\right )^{5} \log \left (x\right ) + 10 \, x \log \left (3\right )^{3} \log \left (x\right )^{2} + 75 \, \log \left (3\right )^{4} \log \left (x\right )^{2} + 2 \, x^{2} \log \left (3\right )^{2} \log \left (x\right ) + 26 \, x \log \left (3\right )^{3} \log \left (x\right ) + 60 \, \log \left (3\right )^{4} \log \left (x\right ) - 25 \, x \log \left (3\right )^{2} \log \left (x\right )^{2} - 125 \, \log \left (3\right )^{3} \log \left (x\right )^{2} + x^{2} \log \left (3\right )^{2} + 6 \, x \log \left (3\right )^{3} + 9 \, \log \left (3\right )^{4} - 10 \, x^{2} \log \left (3\right ) \log \left (x\right ) - 80 \, x \log \left (3\right )^{2} \log \left (x\right ) - 150 \, \log \left (3\right )^{3} \log \left (x\right ) - x^{3} - 11 \, x^{2} \log \left (3\right ) - 39 \, x \log \left (3\right )^{2} - 45 \, \log \left (3\right )^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int -\frac {32\,x+160\,\ln \left (3\right )-32\,{\ln \left (3\right )}^2}{27\,x^2\,{\ln \left (3\right )}^2+\ln \left (x\right )\,\left ({\ln \left (3\right )}^3\,\left (135\,x-18\,x^2\right )+15\,x^3\,\ln \left (3\right )-27\,x\,{\ln \left (3\right )}^4+{\ln \left (3\right )}^2\,\left (90\,x^2-3\,x^3\right )\right )+{\ln \left (x\right )}^3\,\left (125\,x\,{\ln \left (3\right )}^3-75\,x\,{\ln \left (3\right )}^4+15\,x\,{\ln \left (3\right )}^5-x\,{\ln \left (3\right )}^6\right )+27\,x\,{\ln \left (3\right )}^3+9\,x^3\,\ln \left (3\right )+x^4+{\ln \left (x\right )}^2\,\left (75\,x^2\,{\ln \left (3\right )}^2-{\ln \left (3\right )}^4\,\left (90\,x-3\,x^2\right )+{\ln \left (3\right )}^3\,\left (225\,x-30\,x^2\right )+9\,x\,{\ln \left (3\right )}^5\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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