Optimal. Leaf size=56 \[ -\frac{1}{25} (1-x)^{25}+\frac{1}{6} (1-x)^{24}-\frac{6}{23} (1-x)^{23}+\frac{2}{11} (1-x)^{22}-\frac{1}{21} (1-x)^{21} \]
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Rubi [A] time = 0.0252189, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ -\frac{1}{25} (1-x)^{25}+\frac{1}{6} (1-x)^{24}-\frac{6}{23} (1-x)^{23}+\frac{2}{11} (1-x)^{22}-\frac{1}{21} (1-x)^{21} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-x)^{20} x^4 \, dx &=\int \left ((1-x)^{20}-4 (1-x)^{21}+6 (1-x)^{22}-4 (1-x)^{23}+(1-x)^{24}\right ) \, dx\\ &=-\frac{1}{21} (1-x)^{21}+\frac{2}{11} (1-x)^{22}-\frac{6}{23} (1-x)^{23}+\frac{1}{6} (1-x)^{24}-\frac{1}{25} (1-x)^{25}\\ \end{align*}
Mathematica [B] time = 0.0015064, size = 140, normalized size = 2.5 \[ \frac{x^{25}}{25}-\frac{5 x^{24}}{6}+\frac{190 x^{23}}{23}-\frac{570 x^{22}}{11}+\frac{1615 x^{21}}{7}-\frac{3876 x^{20}}{5}+2040 x^{19}-\frac{12920 x^{18}}{3}+7410 x^{17}-\frac{20995 x^{16}}{2}+\frac{184756 x^{15}}{15}-\frac{83980 x^{14}}{7}+9690 x^{13}-6460 x^{12}+\frac{38760 x^{11}}{11}-\frac{7752 x^{10}}{5}+\frac{1615 x^9}{3}-\frac{285 x^8}{2}+\frac{190 x^7}{7}-\frac{10 x^6}{3}+\frac{x^5}{5} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 107, normalized size = 1.9 \begin{align*}{\frac{{x}^{25}}{25}}-{\frac{5\,{x}^{24}}{6}}+{\frac{190\,{x}^{23}}{23}}-{\frac{570\,{x}^{22}}{11}}+{\frac{1615\,{x}^{21}}{7}}-{\frac{3876\,{x}^{20}}{5}}+2040\,{x}^{19}-{\frac{12920\,{x}^{18}}{3}}+7410\,{x}^{17}-{\frac{20995\,{x}^{16}}{2}}+{\frac{184756\,{x}^{15}}{15}}-{\frac{83980\,{x}^{14}}{7}}+9690\,{x}^{13}-6460\,{x}^{12}+{\frac{38760\,{x}^{11}}{11}}-{\frac{7752\,{x}^{10}}{5}}+{\frac{1615\,{x}^{9}}{3}}-{\frac{285\,{x}^{8}}{2}}+{\frac{190\,{x}^{7}}{7}}-{\frac{10\,{x}^{6}}{3}}+{\frac{{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.93812, size = 143, normalized size = 2.55 \begin{align*} \frac{1}{25} \, x^{25} - \frac{5}{6} \, x^{24} + \frac{190}{23} \, x^{23} - \frac{570}{11} \, x^{22} + \frac{1615}{7} \, x^{21} - \frac{3876}{5} \, x^{20} + 2040 \, x^{19} - \frac{12920}{3} \, x^{18} + 7410 \, x^{17} - \frac{20995}{2} \, x^{16} + \frac{184756}{15} \, x^{15} - \frac{83980}{7} \, x^{14} + 9690 \, x^{13} - 6460 \, x^{12} + \frac{38760}{11} \, x^{11} - \frac{7752}{5} \, x^{10} + \frac{1615}{3} \, x^{9} - \frac{285}{2} \, x^{8} + \frac{190}{7} \, x^{7} - \frac{10}{3} \, x^{6} + \frac{1}{5} \, x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.352231, size = 373, normalized size = 6.66 \begin{align*} \frac{1}{25} x^{25} - \frac{5}{6} x^{24} + \frac{190}{23} x^{23} - \frac{570}{11} x^{22} + \frac{1615}{7} x^{21} - \frac{3876}{5} x^{20} + 2040 x^{19} - \frac{12920}{3} x^{18} + 7410 x^{17} - \frac{20995}{2} x^{16} + \frac{184756}{15} x^{15} - \frac{83980}{7} x^{14} + 9690 x^{13} - 6460 x^{12} + \frac{38760}{11} x^{11} - \frac{7752}{5} x^{10} + \frac{1615}{3} x^{9} - \frac{285}{2} x^{8} + \frac{190}{7} x^{7} - \frac{10}{3} x^{6} + \frac{1}{5} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.071957, size = 131, normalized size = 2.34 \begin{align*} \frac{x^{25}}{25} - \frac{5 x^{24}}{6} + \frac{190 x^{23}}{23} - \frac{570 x^{22}}{11} + \frac{1615 x^{21}}{7} - \frac{3876 x^{20}}{5} + 2040 x^{19} - \frac{12920 x^{18}}{3} + 7410 x^{17} - \frac{20995 x^{16}}{2} + \frac{184756 x^{15}}{15} - \frac{83980 x^{14}}{7} + 9690 x^{13} - 6460 x^{12} + \frac{38760 x^{11}}{11} - \frac{7752 x^{10}}{5} + \frac{1615 x^{9}}{3} - \frac{285 x^{8}}{2} + \frac{190 x^{7}}{7} - \frac{10 x^{6}}{3} + \frac{x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.09752, size = 143, normalized size = 2.55 \begin{align*} \frac{1}{25} \, x^{25} - \frac{5}{6} \, x^{24} + \frac{190}{23} \, x^{23} - \frac{570}{11} \, x^{22} + \frac{1615}{7} \, x^{21} - \frac{3876}{5} \, x^{20} + 2040 \, x^{19} - \frac{12920}{3} \, x^{18} + 7410 \, x^{17} - \frac{20995}{2} \, x^{16} + \frac{184756}{15} \, x^{15} - \frac{83980}{7} \, x^{14} + 9690 \, x^{13} - 6460 \, x^{12} + \frac{38760}{11} \, x^{11} - \frac{7752}{5} \, x^{10} + \frac{1615}{3} \, x^{9} - \frac{285}{2} \, x^{8} + \frac{190}{7} \, x^{7} - \frac{10}{3} \, x^{6} + \frac{1}{5} \, x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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