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 = {6688, 12, 6686} \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 6686
Rule 6688
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 = 0.03, 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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fricas [B] time = 1.09, size = 65, normalized size = 3.25 \begin {gather*} \frac {16}{{\left (\log \relax (3)^{4} - 10 \, \log \relax (3)^{3} + 25 \, \log \relax (3)^{2}\right )} \log \relax (x)^{2} + x^{2} + 6 \, x \log \relax (3) + 9 \, \log \relax (3)^{2} - 2 \, {\left ({\left (x - 15\right )} \log \relax (3)^{2} + 3 \, \log \relax (3)^{3} - 5 \, x \log \relax (3)\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 206, normalized size = 10.30 \begin {gather*} \frac {16 \, {\left (\log \relax (3)^{2} - x - 5 \, \log \relax (3)\right )}}{\log \relax (3)^{6} \log \relax (x)^{2} - x \log \relax (3)^{4} \log \relax (x)^{2} - 15 \, \log \relax (3)^{5} \log \relax (x)^{2} - 2 \, x \log \relax (3)^{4} \log \relax (x) - 6 \, \log \relax (3)^{5} \log \relax (x) + 10 \, x \log \relax (3)^{3} \log \relax (x)^{2} + 75 \, \log \relax (3)^{4} \log \relax (x)^{2} + 2 \, x^{2} \log \relax (3)^{2} \log \relax (x) + 26 \, x \log \relax (3)^{3} \log \relax (x) + 60 \, \log \relax (3)^{4} \log \relax (x) - 25 \, x \log \relax (3)^{2} \log \relax (x)^{2} - 125 \, \log \relax (3)^{3} \log \relax (x)^{2} + x^{2} \log \relax (3)^{2} + 6 \, x \log \relax (3)^{3} + 9 \, \log \relax (3)^{4} - 10 \, x^{2} \log \relax (3) \log \relax (x) - 80 \, x \log \relax (3)^{2} \log \relax (x) - 150 \, \log \relax (3)^{3} \log \relax (x) - x^{3} - 11 \, x^{2} \log \relax (3) - 39 \, x \log \relax (3)^{2} - 45 \, \log \relax (3)^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.46, size = 26, normalized size = 1.30
method | result | size |
norman | \(\frac {16}{\left (\ln \relax (3)^{2} \ln \relax (x )-5 \ln \relax (3) \ln \relax (x )-3 \ln \relax (3)-x \right )^{2}}\) | \(26\) |
risch | \(\frac {16}{\left (\ln \relax (3)^{2} \ln \relax (x )-5 \ln \relax (3) \ln \relax (x )-3 \ln \relax (3)-x \right )^{2}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.48, size = 69, normalized size = 3.45 \begin {gather*} \frac {16}{{\left (\log \relax (3)^{4} - 10 \, \log \relax (3)^{3} + 25 \, \log \relax (3)^{2}\right )} \log \relax (x)^{2} + x^{2} + 6 \, x \log \relax (3) + 9 \, \log \relax (3)^{2} - 2 \, {\left (3 \, \log \relax (3)^{3} + {\left (\log \relax (3)^{2} - 5 \, \log \relax (3)\right )} x - 15 \, \log \relax (3)^{2}\right )} \log \relax (x)} \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 \relax (3)-32\,{\ln \relax (3)}^2}{27\,x^2\,{\ln \relax (3)}^2+\ln \relax (x)\,\left ({\ln \relax (3)}^3\,\left (135\,x-18\,x^2\right )+15\,x^3\,\ln \relax (3)-27\,x\,{\ln \relax (3)}^4+{\ln \relax (3)}^2\,\left (90\,x^2-3\,x^3\right )\right )+{\ln \relax (x)}^3\,\left (125\,x\,{\ln \relax (3)}^3-75\,x\,{\ln \relax (3)}^4+15\,x\,{\ln \relax (3)}^5-x\,{\ln \relax (3)}^6\right )+27\,x\,{\ln \relax (3)}^3+9\,x^3\,\ln \relax (3)+x^4+{\ln \relax (x)}^2\,\left (75\,x^2\,{\ln \relax (3)}^2-{\ln \relax (3)}^4\,\left (90\,x-3\,x^2\right )+{\ln \relax (3)}^3\,\left (225\,x-30\,x^2\right )+9\,x\,{\ln \relax (3)}^5\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.40, size = 73, normalized size = 3.65 \begin {gather*} \frac {16}{x^{2} + 6 x \log {\relax (3 )} + \left (- 2 x \log {\relax (3 )}^{2} + 10 x \log {\relax (3 )} - 6 \log {\relax (3 )}^{3} + 30 \log {\relax (3 )}^{2}\right ) \log {\relax (x )} + \left (- 10 \log {\relax (3 )}^{3} + \log {\relax (3 )}^{4} + 25 \log {\relax (3 )}^{2}\right ) \log {\relax (x )}^{2} + 9 \log {\relax (3 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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