Optimal. Leaf size=19 \[ \frac {5}{3 (5+x (3-x+\log (2))+\log (x))^2} \]
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Rubi [A] time = 0.50, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 5, number of rules used = 4, integrand size = 199, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6, 6688, 12, 6686} \begin {gather*} \frac {5}{3 \left (-x^2+x (3+\log (2))+\log (x)+5\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-10+20 x^2+x (-30-10 \log (2))}{375 x+675 x^2+180 x^3-189 x^4-36 x^5+27 x^6-3 x^7+\left (225 x^2+270 x^3-9 x^4-54 x^5+9 x^6\right ) \log (2)+\left (45 x^3+27 x^4-9 x^5\right ) \log ^2(2)+3 x^4 \log ^3(2)+\left (225 x+270 x^2-9 x^3-54 x^4+9 x^5+\left (90 x^2+54 x^3-18 x^4\right ) \log (2)+9 x^3 \log ^2(2)\right ) \log (x)+\left (45 x+27 x^2-9 x^3+9 x^2 \log (2)\right ) \log ^2(x)+3 x \log ^3(x)} \, dx\\ &=\int \frac {-10+20 x^2+x (-30-10 \log (2))}{375 x+675 x^2+180 x^3-36 x^5+27 x^6-3 x^7+\left (225 x^2+270 x^3-9 x^4-54 x^5+9 x^6\right ) \log (2)+\left (45 x^3+27 x^4-9 x^5\right ) \log ^2(2)+x^4 \left (-189+3 \log ^3(2)\right )+\left (225 x+270 x^2-9 x^3-54 x^4+9 x^5+\left (90 x^2+54 x^3-18 x^4\right ) \log (2)+9 x^3 \log ^2(2)\right ) \log (x)+\left (45 x+27 x^2-9 x^3+9 x^2 \log (2)\right ) \log ^2(x)+3 x \log ^3(x)} \, dx\\ &=\int \frac {10 \left (-1+2 x^2-x (3+\log (2))\right )}{3 x \left (5-x^2+x (3+\log (2))+\log (x)\right )^3} \, dx\\ &=\frac {10}{3} \int \frac {-1+2 x^2-x (3+\log (2))}{x \left (5-x^2+x (3+\log (2))+\log (x)\right )^3} \, dx\\ &=\frac {5}{3 \left (5-x^2+x (3+\log (2))+\log (x)\right )^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 21, normalized size = 1.11 \begin {gather*} \frac {5}{3 \left (5-x^2+x (3+\log (2))+\log (x)\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 67, normalized size = 3.53 \begin {gather*} \frac {5}{3 \, {\left (x^{4} + x^{2} \log \relax (2)^{2} - 6 \, x^{3} - x^{2} - 2 \, {\left (x^{3} - 3 \, x^{2} - 5 \, x\right )} \log \relax (2) - 2 \, {\left (x^{2} - x \log \relax (2) - 3 \, x - 5\right )} \log \relax (x) + \log \relax (x)^{2} + 30 \, x + 25\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 215, normalized size = 11.32 \begin {gather*} \frac {5 \, {\left (2 \, x^{2} - x \log \relax (2) - 3 \, x - 1\right )}}{3 \, {\left (2 \, x^{6} - 5 \, x^{5} \log \relax (2) + 4 \, x^{4} \log \relax (2)^{2} - x^{3} \log \relax (2)^{3} - 15 \, x^{5} + 24 \, x^{4} \log \relax (2) - 9 \, x^{3} \log \relax (2)^{2} - 4 \, x^{4} \log \relax (x) + 6 \, x^{3} \log \relax (2) \log \relax (x) - 2 \, x^{2} \log \relax (2)^{2} \log \relax (x) + 15 \, x^{4} + 5 \, x^{3} \log \relax (2) - 11 \, x^{2} \log \relax (2)^{2} + 18 \, x^{3} \log \relax (x) - 12 \, x^{2} \log \relax (2) \log \relax (x) + 2 \, x^{2} \log \relax (x)^{2} - x \log \relax (2) \log \relax (x)^{2} + 69 \, x^{3} - 66 \, x^{2} \log \relax (2) + 4 \, x^{2} \log \relax (x) - 12 \, x \log \relax (2) \log \relax (x) - 3 \, x \log \relax (x)^{2} - 39 \, x^{2} - 35 \, x \log \relax (2) - 36 \, x \log \relax (x) - \log \relax (x)^{2} - 105 \, x - 10 \, \log \relax (x) - 25\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 21, normalized size = 1.11
method | result | size |
risch | \(\frac {5}{3 \left (x \ln \relax (2)-x^{2}+\ln \relax (x )+3 x +5\right )^{2}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.58, size = 59, normalized size = 3.11 \begin {gather*} \frac {5}{3 \, {\left (x^{4} - 2 \, x^{3} {\left (\log \relax (2) + 3\right )} + {\left (\log \relax (2)^{2} + 6 \, \log \relax (2) - 1\right )} x^{2} + 10 \, x {\left (\log \relax (2) + 3\right )} - 2 \, {\left (x^{2} - x {\left (\log \relax (2) + 3\right )} - 5\right )} \log \relax (x) + \log \relax (x)^{2} + 25\right )}} \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 {30\,x+10\,x\,\ln \relax (2)-20\,x^2+10}{375\,x+3\,x^4\,{\ln \relax (2)}^3+3\,x\,{\ln \relax (x)}^3+\ln \relax (x)\,\left (225\,x+9\,x^3\,{\ln \relax (2)}^2+\ln \relax (2)\,\left (-18\,x^4+54\,x^3+90\,x^2\right )+270\,x^2-9\,x^3-54\,x^4+9\,x^5\right )+{\ln \relax (2)}^2\,\left (-9\,x^5+27\,x^4+45\,x^3\right )+\ln \relax (2)\,\left (9\,x^6-54\,x^5-9\,x^4+270\,x^3+225\,x^2\right )+675\,x^2+180\,x^3-189\,x^4-36\,x^5+27\,x^6-3\,x^7+{\ln \relax (x)}^2\,\left (45\,x+9\,x^2\,\ln \relax (2)+27\,x^2-9\,x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.27, size = 82, normalized size = 4.32 \begin {gather*} \frac {5}{3 x^{4} - 18 x^{3} - 6 x^{3} \log {\relax (2 )} - 3 x^{2} + 3 x^{2} \log {\relax (2 )}^{2} + 18 x^{2} \log {\relax (2 )} + 30 x \log {\relax (2 )} + 90 x + \left (- 6 x^{2} + 6 x \log {\relax (2 )} + 18 x + 30\right ) \log {\relax (x )} + 3 \log {\relax (x )}^{2} + 75} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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