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 = 0.03, antiderivative size = 56, normalized size of antiderivative = 1.00, 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*}
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Mathematica [B] time = 0.00, size = 140, normalized size = 2.50 \[ \frac {x^{25}}{25}-\frac {5 x^{24}}{6}+\frac {190 x^{23}}{23}-\frac {570 x^{22}}{11}+\frac {1615 x^{21}}{7}-\frac {3876 x^{20}}{5}+2040 x^{19}-\frac {12920 x^{18}}{3}+7410 x^{17}-\frac {20995 x^{16}}{2}+\frac {184756 x^{15}}{15}-\frac {83980 x^{14}}{7}+9690 x^{13}-6460 x^{12}+\frac {38760 x^{11}}{11}-\frac {7752 x^{10}}{5}+\frac {1615 x^9}{3}-\frac {285 x^8}{2}+\frac {190 x^7}{7}-\frac {10 x^6}{3}+\frac {x^5}{5} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.34, size = 106, normalized size = 1.89 \[ \frac {1}{25} x^{25} - \frac {5}{6} x^{24} + \frac {190}{23} x^{23} - \frac {570}{11} x^{22} + \frac {1615}{7} x^{21} - \frac {3876}{5} x^{20} + 2040 x^{19} - \frac {12920}{3} x^{18} + 7410 x^{17} - \frac {20995}{2} x^{16} + \frac {184756}{15} x^{15} - \frac {83980}{7} x^{14} + 9690 x^{13} - 6460 x^{12} + \frac {38760}{11} x^{11} - \frac {7752}{5} x^{10} + \frac {1615}{3} x^{9} - \frac {285}{2} x^{8} + \frac {190}{7} x^{7} - \frac {10}{3} x^{6} + \frac {1}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.01, size = 106, normalized size = 1.89 \[ \frac {1}{25} \, x^{25} - \frac {5}{6} \, x^{24} + \frac {190}{23} \, x^{23} - \frac {570}{11} \, x^{22} + \frac {1615}{7} \, x^{21} - \frac {3876}{5} \, x^{20} + 2040 \, x^{19} - \frac {12920}{3} \, x^{18} + 7410 \, x^{17} - \frac {20995}{2} \, x^{16} + \frac {184756}{15} \, x^{15} - \frac {83980}{7} \, x^{14} + 9690 \, x^{13} - 6460 \, x^{12} + \frac {38760}{11} \, x^{11} - \frac {7752}{5} \, x^{10} + \frac {1615}{3} \, x^{9} - \frac {285}{2} \, x^{8} + \frac {190}{7} \, x^{7} - \frac {10}{3} \, x^{6} + \frac {1}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 107, normalized size = 1.91 \[ \frac {1}{25} x^{25}-\frac {5}{6} x^{24}+\frac {190}{23} x^{23}-\frac {570}{11} x^{22}+\frac {1615}{7} x^{21}-\frac {3876}{5} x^{20}+2040 x^{19}-\frac {12920}{3} x^{18}+7410 x^{17}-\frac {20995}{2} x^{16}+\frac {184756}{15} x^{15}-\frac {83980}{7} x^{14}+9690 x^{13}-6460 x^{12}+\frac {38760}{11} x^{11}-\frac {7752}{5} x^{10}+\frac {1615}{3} x^{9}-\frac {285}{2} x^{8}+\frac {190}{7} x^{7}-\frac {10}{3} x^{6}+\frac {1}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.61, size = 106, normalized size = 1.89 \[ \frac {1}{25} \, x^{25} - \frac {5}{6} \, x^{24} + \frac {190}{23} \, x^{23} - \frac {570}{11} \, x^{22} + \frac {1615}{7} \, x^{21} - \frac {3876}{5} \, x^{20} + 2040 \, x^{19} - \frac {12920}{3} \, x^{18} + 7410 \, x^{17} - \frac {20995}{2} \, x^{16} + \frac {184756}{15} \, x^{15} - \frac {83980}{7} \, x^{14} + 9690 \, x^{13} - 6460 \, x^{12} + \frac {38760}{11} \, x^{11} - \frac {7752}{5} \, x^{10} + \frac {1615}{3} \, x^{9} - \frac {285}{2} \, x^{8} + \frac {190}{7} \, x^{7} - \frac {10}{3} \, x^{6} + \frac {1}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.46, size = 106, normalized size = 1.89 \[ \frac {x^{25}}{25}-\frac {5\,x^{24}}{6}+\frac {190\,x^{23}}{23}-\frac {570\,x^{22}}{11}+\frac {1615\,x^{21}}{7}-\frac {3876\,x^{20}}{5}+2040\,x^{19}-\frac {12920\,x^{18}}{3}+7410\,x^{17}-\frac {20995\,x^{16}}{2}+\frac {184756\,x^{15}}{15}-\frac {83980\,x^{14}}{7}+9690\,x^{13}-6460\,x^{12}+\frac {38760\,x^{11}}{11}-\frac {7752\,x^{10}}{5}+\frac {1615\,x^9}{3}-\frac {285\,x^8}{2}+\frac {190\,x^7}{7}-\frac {10\,x^6}{3}+\frac {x^5}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 131, normalized size = 2.34 \[ \frac {x^{25}}{25} - \frac {5 x^{24}}{6} + \frac {190 x^{23}}{23} - \frac {570 x^{22}}{11} + \frac {1615 x^{21}}{7} - \frac {3876 x^{20}}{5} + 2040 x^{19} - \frac {12920 x^{18}}{3} + 7410 x^{17} - \frac {20995 x^{16}}{2} + \frac {184756 x^{15}}{15} - \frac {83980 x^{14}}{7} + 9690 x^{13} - 6460 x^{12} + \frac {38760 x^{11}}{11} - \frac {7752 x^{10}}{5} + \frac {1615 x^{9}}{3} - \frac {285 x^{8}}{2} + \frac {190 x^{7}}{7} - \frac {10 x^{6}}{3} + \frac {x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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