Optimal. Leaf size=26 \[ \left (\log (x)+\frac {1}{3} x^2 \log \left (\frac {5}{x}-\frac {5 \log (4)}{x^2}\right )\right )^4 \]
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Rubi [A] time = 0.63, antiderivative size = 27, normalized size of antiderivative = 1.04, number of steps used = 4, number of rules used = 4, integrand size = 284, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {1593, 6688, 12, 6686} \begin {gather*} \frac {1}{81} \left (x^2 \log \left (\frac {5 (x-\log (4))}{x^2}\right )+3 \log (x)\right )^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1593
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (-12 x^7+4 x^9+\left (12 x^6-8 x^8\right ) \log (4)\right ) \log ^3\left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-8 x^9+8 x^8 \log (4)\right ) \log ^4\left (\frac {5 x-5 \log (4)}{x^2}\right )+\log ^3(x) \left (-324 x+108 x^3+\left (324-216 x^2\right ) \log (4)+\left (-216 x^3+216 x^2 \log (4)\right ) \log \left (\frac {5 x-5 \log (4)}{x^2}\right )\right )+\log ^2(x) \left (\left (-324 x^3+108 x^5+\left (324 x^2-216 x^4\right ) \log (4)\right ) \log \left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-216 x^5+216 x^4 \log (4)\right ) \log ^2\left (\frac {5 x-5 \log (4)}{x^2}\right )\right )+\log (x) \left (\left (-108 x^5+36 x^7+\left (108 x^4-72 x^6\right ) \log (4)\right ) \log ^2\left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-72 x^7+72 x^6 \log (4)\right ) \log ^3\left (\frac {5 x-5 \log (4)}{x^2}\right )\right )}{x (-81 x+81 \log (4))} \, dx\\ &=\int \frac {4 \left (3 \log (x)+x^2 \log \left (\frac {5 (x-\log (4))}{x^2}\right )\right )^3 \left (3 x-x^3-3 \log (4)+x^2 \log (16)+2 x^2 (x-\log (4)) \log \left (\frac {5 (x-\log (4))}{x^2}\right )\right )}{81 x (x-\log (4))} \, dx\\ &=\frac {4}{81} \int \frac {\left (3 \log (x)+x^2 \log \left (\frac {5 (x-\log (4))}{x^2}\right )\right )^3 \left (3 x-x^3-3 \log (4)+x^2 \log (16)+2 x^2 (x-\log (4)) \log \left (\frac {5 (x-\log (4))}{x^2}\right )\right )}{x (x-\log (4))} \, dx\\ &=\frac {1}{81} \left (3 \log (x)+x^2 \log \left (\frac {5 (x-\log (4))}{x^2}\right )\right )^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 27, normalized size = 1.04 \begin {gather*} \frac {1}{81} \left (3 \log (x)+x^2 \log \left (\frac {5 (x-\log (4))}{x^2}\right )\right )^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 89, normalized size = 3.42 \begin {gather*} \frac {1}{81} \, x^{8} \log \left (\frac {5 \, {\left (x - 2 \, \log \relax (2)\right )}}{x^{2}}\right )^{4} + \frac {4}{27} \, x^{6} \log \relax (x) \log \left (\frac {5 \, {\left (x - 2 \, \log \relax (2)\right )}}{x^{2}}\right )^{3} + \frac {2}{3} \, x^{4} \log \relax (x)^{2} \log \left (\frac {5 \, {\left (x - 2 \, \log \relax (2)\right )}}{x^{2}}\right )^{2} + \frac {4}{3} \, x^{2} \log \relax (x)^{3} \log \left (\frac {5 \, {\left (x - 2 \, \log \relax (2)\right )}}{x^{2}}\right ) + \log \relax (x)^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.56, size = 140, normalized size = 5.38 \begin {gather*} \frac {1}{81} \, x^{8} \log \left (5 \, x - 10 \, \log \relax (2)\right )^{4} - \frac {4}{81} \, {\left (2 \, x^{8} - 3 \, x^{6}\right )} \log \left (5 \, x - 10 \, \log \relax (2)\right )^{3} \log \relax (x) + \frac {2}{27} \, {\left (4 \, x^{8} - 12 \, x^{6} + 9 \, x^{4}\right )} \log \left (5 \, x - 10 \, \log \relax (2)\right )^{2} \log \relax (x)^{2} - \frac {4}{81} \, {\left (8 \, x^{8} - 36 \, x^{6} + 54 \, x^{4} - 27 \, x^{2}\right )} \log \left (5 \, x - 10 \, \log \relax (2)\right ) \log \relax (x)^{3} + \frac {1}{81} \, {\left (16 \, x^{8} - 96 \, x^{6} + 216 \, x^{4} - 216 \, x^{2} + 81\right )} \log \relax (x)^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 10.66, size = 77075, normalized size = 2964.42
method | result | size |
risch | \(\text {Expression too large to display}\) | \(77075\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.52, size = 333, normalized size = 12.81 \begin {gather*} \frac {1}{81} \, x^{8} \log \relax (5)^{4} + \frac {1}{81} \, x^{8} \log \left (x - 2 \, \log \relax (2)\right )^{4} + \frac {1}{81} \, {\left (16 \, x^{8} - 96 \, x^{6} + 216 \, x^{4} - 216 \, x^{2} + 81\right )} \log \relax (x)^{4} + \frac {4}{81} \, {\left (x^{8} \log \relax (5) - {\left (2 \, x^{8} - 3 \, x^{6}\right )} \log \relax (x)\right )} \log \left (x - 2 \, \log \relax (2)\right )^{3} - \frac {4}{81} \, {\left (8 \, x^{8} \log \relax (5) - 36 \, x^{6} \log \relax (5) + 54 \, x^{4} \log \relax (5) - 27 \, x^{2} \log \relax (5)\right )} \log \relax (x)^{3} + \frac {2}{27} \, {\left (x^{8} \log \relax (5)^{2} + {\left (4 \, x^{8} - 12 \, x^{6} + 9 \, x^{4}\right )} \log \relax (x)^{2} - 2 \, {\left (2 \, x^{8} \log \relax (5) - 3 \, x^{6} \log \relax (5)\right )} \log \relax (x)\right )} \log \left (x - 2 \, \log \relax (2)\right )^{2} + \frac {2}{27} \, {\left (4 \, x^{8} \log \relax (5)^{2} - 12 \, x^{6} \log \relax (5)^{2} + 9 \, x^{4} \log \relax (5)^{2}\right )} \log \relax (x)^{2} + \frac {4}{81} \, {\left (x^{8} \log \relax (5)^{3} - {\left (8 \, x^{8} - 36 \, x^{6} + 54 \, x^{4} - 27 \, x^{2}\right )} \log \relax (x)^{3} + 3 \, {\left (4 \, x^{8} \log \relax (5) - 12 \, x^{6} \log \relax (5) + 9 \, x^{4} \log \relax (5)\right )} \log \relax (x)^{2} - 3 \, {\left (2 \, x^{8} \log \relax (5)^{2} - 3 \, x^{6} \log \relax (5)^{2}\right )} \log \relax (x)\right )} \log \left (x - 2 \, \log \relax (2)\right ) - \frac {4}{81} \, {\left (2 \, x^{8} \log \relax (5)^{3} - 3 \, x^{6} \log \relax (5)^{3}\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 = -0.04 \begin {gather*} \int \frac {\ln \relax (x)\,\left (\left (144\,x^6\,\ln \relax (2)-72\,x^7\right )\,{\ln \left (\frac {5\,x-10\,\ln \relax (2)}{x^2}\right )}^3+\left (2\,\ln \relax (2)\,\left (108\,x^4-72\,x^6\right )-108\,x^5+36\,x^7\right )\,{\ln \left (\frac {5\,x-10\,\ln \relax (2)}{x^2}\right )}^2\right )+{\ln \relax (x)}^2\,\left (\left (432\,x^4\,\ln \relax (2)-216\,x^5\right )\,{\ln \left (\frac {5\,x-10\,\ln \relax (2)}{x^2}\right )}^2+\left (2\,\ln \relax (2)\,\left (324\,x^2-216\,x^4\right )-324\,x^3+108\,x^5\right )\,\ln \left (\frac {5\,x-10\,\ln \relax (2)}{x^2}\right )\right )+{\ln \left (\frac {5\,x-10\,\ln \relax (2)}{x^2}\right )}^4\,\left (16\,x^8\,\ln \relax (2)-8\,x^9\right )-{\ln \relax (x)}^3\,\left (324\,x-\ln \left (\frac {5\,x-10\,\ln \relax (2)}{x^2}\right )\,\left (432\,x^2\,\ln \relax (2)-216\,x^3\right )+2\,\ln \relax (2)\,\left (216\,x^2-324\right )-108\,x^3\right )+{\ln \left (\frac {5\,x-10\,\ln \relax (2)}{x^2}\right )}^3\,\left (2\,\ln \relax (2)\,\left (12\,x^6-8\,x^8\right )-12\,x^7+4\,x^9\right )}{162\,x\,\ln \relax (2)-81\,x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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