Optimal. Leaf size=25 \[ \frac {1}{5} x (2+x+5 (4+x))^2 \left (-x+(-4+\log (x))^2\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(81\) vs. \(2(25)=50\).
time = 0.10, antiderivative size = 81, normalized size of antiderivative = 3.24, number of steps
used = 15, number of rules used = 6, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.128, Rules used = {12, 2403,
2332, 2341, 2333, 2342} \begin {gather*} -\frac {36 x^4}{5}+\frac {312 x^3}{5}+\frac {36}{5} x^3 \log ^2(x)-\frac {288}{5} x^3 \log (x)+748 x^2+\frac {264}{5} x^2 \log ^2(x)-\frac {2112}{5} x^2 \log (x)+\frac {7744 x}{5}+\frac {484}{5} x \log ^2(x)-\frac {3872}{5} x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2332
Rule 2333
Rule 2341
Rule 2342
Rule 2403
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (3872+5368 x+648 x^2-144 x^3+\left (-2904-3696 x-792 x^2\right ) \log (x)+\left (484+528 x+108 x^2\right ) \log ^2(x)\right ) \, dx\\ &=\frac {3872 x}{5}+\frac {2684 x^2}{5}+\frac {216 x^3}{5}-\frac {36 x^4}{5}+\frac {1}{5} \int \left (-2904-3696 x-792 x^2\right ) \log (x) \, dx+\frac {1}{5} \int \left (484+528 x+108 x^2\right ) \log ^2(x) \, dx\\ &=\frac {3872 x}{5}+\frac {2684 x^2}{5}+\frac {216 x^3}{5}-\frac {36 x^4}{5}+\frac {1}{5} \int \left (-2904 \log (x)-3696 x \log (x)-792 x^2 \log (x)\right ) \, dx+\frac {1}{5} \int \left (484 \log ^2(x)+528 x \log ^2(x)+108 x^2 \log ^2(x)\right ) \, dx\\ &=\frac {3872 x}{5}+\frac {2684 x^2}{5}+\frac {216 x^3}{5}-\frac {36 x^4}{5}+\frac {108}{5} \int x^2 \log ^2(x) \, dx+\frac {484}{5} \int \log ^2(x) \, dx+\frac {528}{5} \int x \log ^2(x) \, dx-\frac {792}{5} \int x^2 \log (x) \, dx-\frac {2904}{5} \int \log (x) \, dx-\frac {3696}{5} \int x \log (x) \, dx\\ &=\frac {6776 x}{5}+\frac {3608 x^2}{5}+\frac {304 x^3}{5}-\frac {36 x^4}{5}-\frac {2904}{5} x \log (x)-\frac {1848}{5} x^2 \log (x)-\frac {264}{5} x^3 \log (x)+\frac {484}{5} x \log ^2(x)+\frac {264}{5} x^2 \log ^2(x)+\frac {36}{5} x^3 \log ^2(x)-\frac {72}{5} \int x^2 \log (x) \, dx-\frac {528}{5} \int x \log (x) \, dx-\frac {968}{5} \int \log (x) \, dx\\ &=\frac {7744 x}{5}+748 x^2+\frac {312 x^3}{5}-\frac {36 x^4}{5}-\frac {3872}{5} x \log (x)-\frac {2112}{5} x^2 \log (x)-\frac {288}{5} x^3 \log (x)+\frac {484}{5} x \log ^2(x)+\frac {264}{5} x^2 \log ^2(x)+\frac {36}{5} x^3 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 25, normalized size = 1.00 \begin {gather*} -\frac {4}{5} x (11+3 x)^2 \left (-16+x+8 \log (x)-\log ^2(x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(63\) vs.
\(2(20)=40\).
time = 0.12, size = 64, normalized size = 2.56
method | result | size |
default | \(\frac {7744 x}{5}+748 x^{2}+\frac {312 x^{3}}{5}-\frac {36 x^{4}}{5}-\frac {288 x^{3} \ln \left (x \right )}{5}-\frac {2112 x^{2} \ln \left (x \right )}{5}-\frac {3872 x \ln \left (x \right )}{5}+\frac {36 x^{3} \ln \left (x \right )^{2}}{5}+\frac {264 x^{2} \ln \left (x \right )^{2}}{5}+\frac {484 x \ln \left (x \right )^{2}}{5}\) | \(64\) |
norman | \(\frac {7744 x}{5}+748 x^{2}+\frac {312 x^{3}}{5}-\frac {36 x^{4}}{5}-\frac {288 x^{3} \ln \left (x \right )}{5}-\frac {2112 x^{2} \ln \left (x \right )}{5}-\frac {3872 x \ln \left (x \right )}{5}+\frac {36 x^{3} \ln \left (x \right )^{2}}{5}+\frac {264 x^{2} \ln \left (x \right )^{2}}{5}+\frac {484 x \ln \left (x \right )^{2}}{5}\) | \(64\) |
risch | \(\frac {7744 x}{5}+748 x^{2}+\frac {312 x^{3}}{5}-\frac {36 x^{4}}{5}-\frac {288 x^{3} \ln \left (x \right )}{5}-\frac {2112 x^{2} \ln \left (x \right )}{5}-\frac {3872 x \ln \left (x \right )}{5}+\frac {36 x^{3} \ln \left (x \right )^{2}}{5}+\frac {264 x^{2} \ln \left (x \right )^{2}}{5}+\frac {484 x \ln \left (x \right )^{2}}{5}\) | \(64\) |
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. 82 vs.
\(2 (20) = 40\).
time = 0.26, size = 82, normalized size = 3.28 \begin {gather*} \frac {4}{5} \, {\left (9 \, \log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 2\right )} x^{3} - \frac {36}{5} \, x^{4} + \frac {132}{5} \, {\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} + \frac {304}{5} \, x^{3} + \frac {484}{5} \, {\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x + \frac {3608}{5} \, x^{2} - \frac {264}{5} \, {\left (x^{3} + 7 \, x^{2} + 11 \, x\right )} \log \left (x\right ) + \frac {6776}{5} \, x \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. 57 vs.
\(2 (20) = 40\).
time = 0.38, size = 57, normalized size = 2.28 \begin {gather*} -\frac {36}{5} \, x^{4} + \frac {312}{5} \, x^{3} + \frac {4}{5} \, {\left (9 \, x^{3} + 66 \, x^{2} + 121 \, x\right )} \log \left (x\right )^{2} + 748 \, x^{2} - \frac {32}{5} \, {\left (9 \, x^{3} + 66 \, x^{2} + 121 \, x\right )} \log \left (x\right ) + \frac {7744}{5} \, x \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. 70 vs.
\(2 (19) = 38\).
time = 0.08, size = 70, normalized size = 2.80 \begin {gather*} - \frac {36 x^{4}}{5} + \frac {312 x^{3}}{5} + 748 x^{2} + \frac {7744 x}{5} + \left (- \frac {288 x^{3}}{5} - \frac {2112 x^{2}}{5} - \frac {3872 x}{5}\right ) \log {\left (x \right )} + \left (\frac {36 x^{3}}{5} + \frac {264 x^{2}}{5} + \frac {484 x}{5}\right ) \log {\left (x \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. 63 vs.
\(2 (20) = 40\).
time = 0.39, size = 63, normalized size = 2.52 \begin {gather*} \frac {36}{5} \, x^{3} \log \left (x\right )^{2} - \frac {36}{5} \, x^{4} - \frac {288}{5} \, x^{3} \log \left (x\right ) + \frac {264}{5} \, x^{2} \log \left (x\right )^{2} + \frac {312}{5} \, x^{3} - \frac {2112}{5} \, x^{2} \log \left (x\right ) + \frac {484}{5} \, x \log \left (x\right )^{2} + 748 \, x^{2} - \frac {3872}{5} \, x \log \left (x\right ) + \frac {7744}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.04, size = 23, normalized size = 0.92 \begin {gather*} -\frac {4\,x\,{\left (3\,x+11\right )}^2\,\left (-{\ln \left (x\right )}^2+8\,\ln \left (x\right )+x-16\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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