Optimal. Leaf size=127 \[ -\frac{6237 x^{10}}{156250000}+\frac{1}{10} x^{10} \log ^{11}(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{11}{100} x^{10} \log ^9(x)-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{2079 x^{10} \log ^4(x)}{125000}+\frac{2079 x^{10} \log ^3(x)}{312500}-\frac{6237 x^{10} \log ^2(x)}{3125000}+\frac{6237 x^{10} \log (x)}{15625000} \]
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Rubi [A] time = 0.141166, antiderivative size = 127, normalized size of antiderivative = 1., number of steps used = 11, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {2305, 2304} \[ -\frac{6237 x^{10}}{156250000}+\frac{1}{10} x^{10} \log ^{11}(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{11}{100} x^{10} \log ^9(x)-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{2079 x^{10} \log ^4(x)}{125000}+\frac{2079 x^{10} \log ^3(x)}{312500}-\frac{6237 x^{10} \log ^2(x)}{3125000}+\frac{6237 x^{10} \log (x)}{15625000} \]
Antiderivative was successfully verified.
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Rule 2305
Rule 2304
Rubi steps
\begin{align*} \int x^9 \log ^{11}(x) \, dx &=\frac{1}{10} x^{10} \log ^{11}(x)-\frac{11}{10} \int x^9 \log ^{10}(x) \, dx\\ &=-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)+\frac{11}{10} \int x^9 \log ^9(x) \, dx\\ &=\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)-\frac{99}{100} \int x^9 \log ^8(x) \, dx\\ &=-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)+\frac{99}{125} \int x^9 \log ^7(x) \, dx\\ &=\frac{99 x^{10} \log ^7(x)}{1250}-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)-\frac{693 \int x^9 \log ^6(x) \, dx}{1250}\\ &=-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)+\frac{2079 \int x^9 \log ^5(x) \, dx}{6250}\\ &=\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)-\frac{2079 \int x^9 \log ^4(x) \, dx}{12500}\\ &=-\frac{2079 x^{10} \log ^4(x)}{125000}+\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)+\frac{2079 \int x^9 \log ^3(x) \, dx}{31250}\\ &=\frac{2079 x^{10} \log ^3(x)}{312500}-\frac{2079 x^{10} \log ^4(x)}{125000}+\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)-\frac{6237 \int x^9 \log ^2(x) \, dx}{312500}\\ &=-\frac{6237 x^{10} \log ^2(x)}{3125000}+\frac{2079 x^{10} \log ^3(x)}{312500}-\frac{2079 x^{10} \log ^4(x)}{125000}+\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)+\frac{6237 \int x^9 \log (x) \, dx}{1562500}\\ &=-\frac{6237 x^{10}}{156250000}+\frac{6237 x^{10} \log (x)}{15625000}-\frac{6237 x^{10} \log ^2(x)}{3125000}+\frac{2079 x^{10} \log ^3(x)}{312500}-\frac{2079 x^{10} \log ^4(x)}{125000}+\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{11}{100} x^{10} \log ^9(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{1}{10} x^{10} \log ^{11}(x)\\ \end{align*}
Mathematica [A] time = 0.0032175, size = 127, normalized size = 1. \[ -\frac{6237 x^{10}}{156250000}+\frac{1}{10} x^{10} \log ^{11}(x)-\frac{11}{100} x^{10} \log ^{10}(x)+\frac{11}{100} x^{10} \log ^9(x)-\frac{99 x^{10} \log ^8(x)}{1000}+\frac{99 x^{10} \log ^7(x)}{1250}-\frac{693 x^{10} \log ^6(x)}{12500}+\frac{2079 x^{10} \log ^5(x)}{62500}-\frac{2079 x^{10} \log ^4(x)}{125000}+\frac{2079 x^{10} \log ^3(x)}{312500}-\frac{6237 x^{10} \log ^2(x)}{3125000}+\frac{6237 x^{10} \log (x)}{15625000} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 104, normalized size = 0.8 \begin{align*} -{\frac{6237\,{x}^{10}}{156250000}}+{\frac{6237\,{x}^{10}\ln \left ( x \right ) }{15625000}}-{\frac{6237\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{2}}{3125000}}+{\frac{2079\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{3}}{312500}}-{\frac{2079\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{4}}{125000}}+{\frac{2079\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{5}}{62500}}-{\frac{693\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{6}}{12500}}+{\frac{99\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{7}}{1250}}-{\frac{99\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{8}}{1000}}+{\frac{11\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{9}}{100}}-{\frac{11\,{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{10}}{100}}+{\frac{{x}^{10} \left ( \ln \left ( x \right ) \right ) ^{11}}{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936561, size = 96, normalized size = 0.76 \begin{align*} \frac{1}{156250000} \,{\left (15625000 \, \log \left (x\right )^{11} - 17187500 \, \log \left (x\right )^{10} + 17187500 \, \log \left (x\right )^{9} - 15468750 \, \log \left (x\right )^{8} + 12375000 \, \log \left (x\right )^{7} - 8662500 \, \log \left (x\right )^{6} + 5197500 \, \log \left (x\right )^{5} - 2598750 \, \log \left (x\right )^{4} + 1039500 \, \log \left (x\right )^{3} - 311850 \, \log \left (x\right )^{2} + 62370 \, \log \left (x\right ) - 6237\right )} x^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.05302, size = 410, normalized size = 3.23 \begin{align*} \frac{1}{10} \, x^{10} \log \left (x\right )^{11} - \frac{11}{100} \, x^{10} \log \left (x\right )^{10} + \frac{11}{100} \, x^{10} \log \left (x\right )^{9} - \frac{99}{1000} \, x^{10} \log \left (x\right )^{8} + \frac{99}{1250} \, x^{10} \log \left (x\right )^{7} - \frac{693}{12500} \, x^{10} \log \left (x\right )^{6} + \frac{2079}{62500} \, x^{10} \log \left (x\right )^{5} - \frac{2079}{125000} \, x^{10} \log \left (x\right )^{4} + \frac{2079}{312500} \, x^{10} \log \left (x\right )^{3} - \frac{6237}{3125000} \, x^{10} \log \left (x\right )^{2} + \frac{6237}{15625000} \, x^{10} \log \left (x\right ) - \frac{6237}{156250000} \, x^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.262542, size = 133, normalized size = 1.05 \begin{align*} \frac{x^{10} \log{\left (x \right )}^{11}}{10} - \frac{11 x^{10} \log{\left (x \right )}^{10}}{100} + \frac{11 x^{10} \log{\left (x \right )}^{9}}{100} - \frac{99 x^{10} \log{\left (x \right )}^{8}}{1000} + \frac{99 x^{10} \log{\left (x \right )}^{7}}{1250} - \frac{693 x^{10} \log{\left (x \right )}^{6}}{12500} + \frac{2079 x^{10} \log{\left (x \right )}^{5}}{62500} - \frac{2079 x^{10} \log{\left (x \right )}^{4}}{125000} + \frac{2079 x^{10} \log{\left (x \right )}^{3}}{312500} - \frac{6237 x^{10} \log{\left (x \right )}^{2}}{3125000} + \frac{6237 x^{10} \log{\left (x \right )}}{15625000} - \frac{6237 x^{10}}{156250000} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07493, size = 139, normalized size = 1.09 \begin{align*} \frac{1}{10} \, x^{10} \log \left (x\right )^{11} - \frac{11}{100} \, x^{10} \log \left (x\right )^{10} + \frac{11}{100} \, x^{10} \log \left (x\right )^{9} - \frac{99}{1000} \, x^{10} \log \left (x\right )^{8} + \frac{99}{1250} \, x^{10} \log \left (x\right )^{7} - \frac{693}{12500} \, x^{10} \log \left (x\right )^{6} + \frac{2079}{62500} \, x^{10} \log \left (x\right )^{5} - \frac{2079}{125000} \, x^{10} \log \left (x\right )^{4} + \frac{2079}{312500} \, x^{10} \log \left (x\right )^{3} - \frac{6237}{3125000} \, x^{10} \log \left (x\right )^{2} + \frac{6237}{15625000} \, x^{10} \log \left (x\right ) - \frac{6237}{156250000} \, x^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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