Optimal. Leaf size=21 \[ (2+x-(-1+x) x (x+(-3+5 x) \log (x)))^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(112\) vs. \(2(21)=42\).
time = 0.21, antiderivative size = 112, normalized size of antiderivative = 5.33, number of steps
used = 21, number of rules used = 4, integrand size = 82, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {2403, 2332,
2341, 2342} \begin {gather*} x^6+25 x^6 \log ^2(x)+10 x^6 \log (x)-2 x^5-80 x^5 \log ^2(x)-26 x^5 \log (x)-x^4+94 x^4 \log ^2(x)+12 x^4 \log (x)-2 x^3-48 x^3 \log ^2(x)-10 x^3 \log (x)+5 x^2+9 x^2 \log ^2(x)+26 x^2 \log (x)+4 x-12 x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2332
Rule 2341
Rule 2342
Rule 2403
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-8 x+18 x^2-\frac {16 x^3}{3}+2 x^4-\frac {36 x^5}{5}+\frac {8 x^6}{3}+\int \left (-12+70 x-126 x^2+236 x^3-290 x^4+110 x^5\right ) \log (x) \, dx+\int \left (18 x-144 x^2+376 x^3-400 x^4+150 x^5\right ) \log ^2(x) \, dx\\ &=-8 x+18 x^2-\frac {16 x^3}{3}+2 x^4-\frac {36 x^5}{5}+\frac {8 x^6}{3}+\int \left (-12 \log (x)+70 x \log (x)-126 x^2 \log (x)+236 x^3 \log (x)-290 x^4 \log (x)+110 x^5 \log (x)\right ) \, dx+\int \left (18 x \log ^2(x)-144 x^2 \log ^2(x)+376 x^3 \log ^2(x)-400 x^4 \log ^2(x)+150 x^5 \log ^2(x)\right ) \, dx\\ &=-8 x+18 x^2-\frac {16 x^3}{3}+2 x^4-\frac {36 x^5}{5}+\frac {8 x^6}{3}-12 \int \log (x) \, dx+18 \int x \log ^2(x) \, dx+70 \int x \log (x) \, dx+110 \int x^5 \log (x) \, dx-126 \int x^2 \log (x) \, dx-144 \int x^2 \log ^2(x) \, dx+150 \int x^5 \log ^2(x) \, dx+236 \int x^3 \log (x) \, dx-290 \int x^4 \log (x) \, dx+376 \int x^3 \log ^2(x) \, dx-400 \int x^4 \log ^2(x) \, dx\\ &=4 x+\frac {x^2}{2}+\frac {26 x^3}{3}-\frac {51 x^4}{4}+\frac {22 x^5}{5}-\frac {7 x^6}{18}-12 x \log (x)+35 x^2 \log (x)-42 x^3 \log (x)+59 x^4 \log (x)-58 x^5 \log (x)+\frac {55}{3} x^6 \log (x)+9 x^2 \log ^2(x)-48 x^3 \log ^2(x)+94 x^4 \log ^2(x)-80 x^5 \log ^2(x)+25 x^6 \log ^2(x)-18 \int x \log (x) \, dx-50 \int x^5 \log (x) \, dx+96 \int x^2 \log (x) \, dx+160 \int x^4 \log (x) \, dx-188 \int x^3 \log (x) \, dx\\ &=4 x+5 x^2-2 x^3-x^4-2 x^5+x^6-12 x \log (x)+26 x^2 \log (x)-10 x^3 \log (x)+12 x^4 \log (x)-26 x^5 \log (x)+10 x^6 \log (x)+9 x^2 \log ^2(x)-48 x^3 \log ^2(x)+94 x^4 \log ^2(x)-80 x^5 \log ^2(x)+25 x^6 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(112\) vs. \(2(21)=42\).
time = 0.04, size = 112, normalized size = 5.33 \begin {gather*} 4 x+5 x^2-2 x^3-x^4-2 x^5+x^6-12 x \log (x)+26 x^2 \log (x)-10 x^3 \log (x)+12 x^4 \log (x)-26 x^5 \log (x)+10 x^6 \log (x)+9 x^2 \log ^2(x)-48 x^3 \log ^2(x)+94 x^4 \log ^2(x)-80 x^5 \log ^2(x)+25 x^6 \log ^2(x) \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. \(112\) vs.
\(2(21)=42\).
time = 0.21, size = 113, normalized size = 5.38
method | result | size |
default | \(4 x +25 x^{6} \ln \left (x \right )^{2}+10 x^{6} \ln \left (x \right )-26 x^{5} \ln \left (x \right )+94 x^{4} \ln \left (x \right )^{2}+12 x^{4} \ln \left (x \right )-12 x \ln \left (x \right )-80 x^{5} \ln \left (x \right )^{2}-48 x^{3} \ln \left (x \right )^{2}+9 x^{2} \ln \left (x \right )^{2}-10 x^{3} \ln \left (x \right )+26 x^{2} \ln \left (x \right )+x^{6}-2 x^{5}-x^{4}-2 x^{3}+5 x^{2}\) | \(113\) |
norman | \(4 x +25 x^{6} \ln \left (x \right )^{2}+10 x^{6} \ln \left (x \right )-26 x^{5} \ln \left (x \right )+94 x^{4} \ln \left (x \right )^{2}+12 x^{4} \ln \left (x \right )-12 x \ln \left (x \right )-80 x^{5} \ln \left (x \right )^{2}-48 x^{3} \ln \left (x \right )^{2}+9 x^{2} \ln \left (x \right )^{2}-10 x^{3} \ln \left (x \right )+26 x^{2} \ln \left (x \right )+x^{6}-2 x^{5}-x^{4}-2 x^{3}+5 x^{2}\) | \(113\) |
risch | \(\left (25 x^{6}-80 x^{5}+94 x^{4}-48 x^{3}+9 x^{2}\right ) \ln \left (x \right )^{2}+\left (-\frac {25}{3} x^{6}+32 x^{5}-47 x^{4}+32 x^{3}-9 x^{2}\right ) \ln \left (x \right )+x^{6}-2 x^{5}-x^{4}-2 x^{3}+5 x^{2}+\left (\frac {55}{3} x^{6}-58 x^{5}+59 x^{4}-42 x^{3}+35 x^{2}-12 x \right ) \ln \left (x \right )+4 x\) | \(120\) |
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. 147 vs.
\(2 (22) = 44\).
time = 0.27, size = 147, normalized size = 7.00 \begin {gather*} \frac {25}{18} \, {\left (18 \, \log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 1\right )} x^{6} - \frac {16}{5} \, {\left (25 \, \log \left (x\right )^{2} - 10 \, \log \left (x\right ) + 2\right )} x^{5} - \frac {7}{18} \, x^{6} + \frac {47}{4} \, {\left (8 \, \log \left (x\right )^{2} - 4 \, \log \left (x\right ) + 1\right )} x^{4} + \frac {22}{5} \, x^{5} - \frac {16}{3} \, {\left (9 \, \log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 2\right )} x^{3} - \frac {51}{4} \, x^{4} + \frac {9}{2} \, {\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} + \frac {26}{3} \, x^{3} + \frac {1}{2} \, x^{2} + \frac {1}{3} \, {\left (55 \, x^{6} - 174 \, x^{5} + 177 \, x^{4} - 126 \, x^{3} + 105 \, x^{2} - 36 \, x\right )} \log \left (x\right ) + 4 \, 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. 91 vs.
\(2 (22) = 44\).
time = 0.38, size = 91, normalized size = 4.33 \begin {gather*} x^{6} - 2 \, x^{5} - x^{4} - 2 \, x^{3} + {\left (25 \, x^{6} - 80 \, x^{5} + 94 \, x^{4} - 48 \, x^{3} + 9 \, x^{2}\right )} \log \left (x\right )^{2} + 5 \, x^{2} + 2 \, {\left (5 \, x^{6} - 13 \, x^{5} + 6 \, x^{4} - 5 \, x^{3} + 13 \, x^{2} - 6 \, x\right )} \log \left (x\right ) + 4 \, 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. 87 vs.
\(2 (19) = 38\).
time = 0.09, size = 87, normalized size = 4.14 \begin {gather*} x^{6} - 2 x^{5} - x^{4} - 2 x^{3} + 5 x^{2} + 4 x + \left (25 x^{6} - 80 x^{5} + 94 x^{4} - 48 x^{3} + 9 x^{2}\right ) \log {\left (x \right )}^{2} + \left (10 x^{6} - 26 x^{5} + 12 x^{4} - 10 x^{3} + 26 x^{2} - 12 x\right ) \log {\left (x \right )} \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. 112 vs.
\(2 (22) = 44\).
time = 0.42, size = 112, normalized size = 5.33 \begin {gather*} 25 \, x^{6} \log \left (x\right )^{2} + 10 \, x^{6} \log \left (x\right ) - 80 \, x^{5} \log \left (x\right )^{2} + x^{6} - 26 \, x^{5} \log \left (x\right ) + 94 \, x^{4} \log \left (x\right )^{2} - 2 \, x^{5} + 12 \, x^{4} \log \left (x\right ) - 48 \, x^{3} \log \left (x\right )^{2} - x^{4} - 10 \, x^{3} \log \left (x\right ) + 9 \, x^{2} \log \left (x\right )^{2} - 2 \, x^{3} + 26 \, x^{2} \log \left (x\right ) + 5 \, x^{2} - 12 \, x \log \left (x\right ) + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.63, size = 112, normalized size = 5.33 \begin {gather*} 25\,x^6\,{\ln \left (x\right )}^2+10\,x^6\,\ln \left (x\right )+x^6-80\,x^5\,{\ln \left (x\right )}^2-26\,x^5\,\ln \left (x\right )-2\,x^5+94\,x^4\,{\ln \left (x\right )}^2+12\,x^4\,\ln \left (x\right )-x^4-48\,x^3\,{\ln \left (x\right )}^2-10\,x^3\,\ln \left (x\right )-2\,x^3+9\,x^2\,{\ln \left (x\right )}^2+26\,x^2\,\ln \left (x\right )+5\,x^2-12\,x\,\ln \left (x\right )+4\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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