Integrand size = 11, antiderivative size = 56 \[ \int (1-x)^{20} x^4 \, dx=-\frac {1}{21} (1-x)^{21}+\frac {2}{11} (1-x)^{22}-\frac {6}{23} (1-x)^{23}+\frac {1}{6} (1-x)^{24}-\frac {1}{25} (1-x)^{25} \]
[Out]
Time = 0.02 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45} \[ \int (1-x)^{20} x^4 \, dx=-\frac {1}{25} (1-x)^{25}+\frac {1}{6} (1-x)^{24}-\frac {6}{23} (1-x)^{23}+\frac {2}{11} (1-x)^{22}-\frac {1}{21} (1-x)^{21} \]
[In]
[Out]
Rule 45
Rubi steps \begin{align*} \text {integral}& = \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*}
Leaf count is larger than twice the leaf count of optimal. \(140\) vs. \(2(56)=112\).
Time = 0.00 (sec) , antiderivative size = 140, normalized size of antiderivative = 2.50 \[ \int (1-x)^{20} x^4 \, dx=\frac {x^5}{5}-\frac {10 x^6}{3}+\frac {190 x^7}{7}-\frac {285 x^8}{2}+\frac {1615 x^9}{3}-\frac {7752 x^{10}}{5}+\frac {38760 x^{11}}{11}-6460 x^{12}+9690 x^{13}-\frac {83980 x^{14}}{7}+\frac {184756 x^{15}}{15}-\frac {20995 x^{16}}{2}+7410 x^{17}-\frac {12920 x^{18}}{3}+2040 x^{19}-\frac {3876 x^{20}}{5}+\frac {1615 x^{21}}{7}-\frac {570 x^{22}}{11}+\frac {190 x^{23}}{23}-\frac {5 x^{24}}{6}+\frac {x^{25}}{25} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(105\) vs. \(2(46)=92\).
Time = 0.04 (sec) , antiderivative size = 106, normalized size of antiderivative = 1.89
method | result | size |
gosper | \(\frac {x^{5} \left (10626 x^{20}-221375 x^{19}+2194500 x^{18}-13765500 x^{17}+61289250 x^{16}-205931880 x^{15}+541926000 x^{14}-1144066000 x^{13}+1968466500 x^{12}-2788660875 x^{11}+3272028760 x^{10}-3187041000 x^{9}+2574148500 x^{8}-1716099000 x^{7}+936054000 x^{6}-411863760 x^{5}+143008250 x^{4}-37855125 x^{3}+7210500 x^{2}-885500 x +53130\right )}{265650}\) | \(106\) |
default | \(\frac {1}{5} x^{5}-\frac {10}{3} x^{6}+\frac {190}{7} x^{7}-\frac {285}{2} x^{8}+\frac {1615}{3} x^{9}-\frac {7752}{5} x^{10}+\frac {38760}{11} x^{11}-6460 x^{12}+9690 x^{13}-\frac {83980}{7} x^{14}+\frac {184756}{15} x^{15}-\frac {20995}{2} x^{16}+7410 x^{17}-\frac {12920}{3} x^{18}+2040 x^{19}-\frac {3876}{5} x^{20}+\frac {1615}{7} x^{21}-\frac {570}{11} x^{22}+\frac {190}{23} x^{23}-\frac {5}{6} x^{24}+\frac {1}{25} x^{25}\) | \(107\) |
norman | \(\frac {1}{5} x^{5}-\frac {10}{3} x^{6}+\frac {190}{7} x^{7}-\frac {285}{2} x^{8}+\frac {1615}{3} x^{9}-\frac {7752}{5} x^{10}+\frac {38760}{11} x^{11}-6460 x^{12}+9690 x^{13}-\frac {83980}{7} x^{14}+\frac {184756}{15} x^{15}-\frac {20995}{2} x^{16}+7410 x^{17}-\frac {12920}{3} x^{18}+2040 x^{19}-\frac {3876}{5} x^{20}+\frac {1615}{7} x^{21}-\frac {570}{11} x^{22}+\frac {190}{23} x^{23}-\frac {5}{6} x^{24}+\frac {1}{25} x^{25}\) | \(107\) |
risch | \(\frac {1}{5} x^{5}-\frac {10}{3} x^{6}+\frac {190}{7} x^{7}-\frac {285}{2} x^{8}+\frac {1615}{3} x^{9}-\frac {7752}{5} x^{10}+\frac {38760}{11} x^{11}-6460 x^{12}+9690 x^{13}-\frac {83980}{7} x^{14}+\frac {184756}{15} x^{15}-\frac {20995}{2} x^{16}+7410 x^{17}-\frac {12920}{3} x^{18}+2040 x^{19}-\frac {3876}{5} x^{20}+\frac {1615}{7} x^{21}-\frac {570}{11} x^{22}+\frac {190}{23} x^{23}-\frac {5}{6} x^{24}+\frac {1}{25} x^{25}\) | \(107\) |
parallelrisch | \(\frac {1}{5} x^{5}-\frac {10}{3} x^{6}+\frac {190}{7} x^{7}-\frac {285}{2} x^{8}+\frac {1615}{3} x^{9}-\frac {7752}{5} x^{10}+\frac {38760}{11} x^{11}-6460 x^{12}+9690 x^{13}-\frac {83980}{7} x^{14}+\frac {184756}{15} x^{15}-\frac {20995}{2} x^{16}+7410 x^{17}-\frac {12920}{3} x^{18}+2040 x^{19}-\frac {3876}{5} x^{20}+\frac {1615}{7} x^{21}-\frac {570}{11} x^{22}+\frac {190}{23} x^{23}-\frac {5}{6} x^{24}+\frac {1}{25} x^{25}\) | \(107\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (36) = 72\).
Time = 0.23 (sec) , antiderivative size = 106, normalized size of antiderivative = 1.89 \[ \int (1-x)^{20} x^4 \, dx=\frac {1}{25} \, x^{25} - \frac {5}{6} \, x^{24} + \frac {190}{23} \, x^{23} - \frac {570}{11} \, x^{22} + \frac {1615}{7} \, x^{21} - \frac {3876}{5} \, x^{20} + 2040 \, x^{19} - \frac {12920}{3} \, x^{18} + 7410 \, x^{17} - \frac {20995}{2} \, x^{16} + \frac {184756}{15} \, x^{15} - \frac {83980}{7} \, x^{14} + 9690 \, x^{13} - 6460 \, x^{12} + \frac {38760}{11} \, x^{11} - \frac {7752}{5} \, x^{10} + \frac {1615}{3} \, x^{9} - \frac {285}{2} \, x^{8} + \frac {190}{7} \, x^{7} - \frac {10}{3} \, x^{6} + \frac {1}{5} \, x^{5} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (36) = 72\).
Time = 0.04 (sec) , antiderivative size = 131, normalized size of antiderivative = 2.34 \[ \int (1-x)^{20} x^4 \, dx=\frac {x^{25}}{25} - \frac {5 x^{24}}{6} + \frac {190 x^{23}}{23} - \frac {570 x^{22}}{11} + \frac {1615 x^{21}}{7} - \frac {3876 x^{20}}{5} + 2040 x^{19} - \frac {12920 x^{18}}{3} + 7410 x^{17} - \frac {20995 x^{16}}{2} + \frac {184756 x^{15}}{15} - \frac {83980 x^{14}}{7} + 9690 x^{13} - 6460 x^{12} + \frac {38760 x^{11}}{11} - \frac {7752 x^{10}}{5} + \frac {1615 x^{9}}{3} - \frac {285 x^{8}}{2} + \frac {190 x^{7}}{7} - \frac {10 x^{6}}{3} + \frac {x^{5}}{5} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (36) = 72\).
Time = 0.18 (sec) , antiderivative size = 106, normalized size of antiderivative = 1.89 \[ \int (1-x)^{20} x^4 \, dx=\frac {1}{25} \, x^{25} - \frac {5}{6} \, x^{24} + \frac {190}{23} \, x^{23} - \frac {570}{11} \, x^{22} + \frac {1615}{7} \, x^{21} - \frac {3876}{5} \, x^{20} + 2040 \, x^{19} - \frac {12920}{3} \, x^{18} + 7410 \, x^{17} - \frac {20995}{2} \, x^{16} + \frac {184756}{15} \, x^{15} - \frac {83980}{7} \, x^{14} + 9690 \, x^{13} - 6460 \, x^{12} + \frac {38760}{11} \, x^{11} - \frac {7752}{5} \, x^{10} + \frac {1615}{3} \, x^{9} - \frac {285}{2} \, x^{8} + \frac {190}{7} \, x^{7} - \frac {10}{3} \, x^{6} + \frac {1}{5} \, x^{5} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (36) = 72\).
Time = 0.26 (sec) , antiderivative size = 106, normalized size of antiderivative = 1.89 \[ \int (1-x)^{20} x^4 \, dx=\frac {1}{25} \, x^{25} - \frac {5}{6} \, x^{24} + \frac {190}{23} \, x^{23} - \frac {570}{11} \, x^{22} + \frac {1615}{7} \, x^{21} - \frac {3876}{5} \, x^{20} + 2040 \, x^{19} - \frac {12920}{3} \, x^{18} + 7410 \, x^{17} - \frac {20995}{2} \, x^{16} + \frac {184756}{15} \, x^{15} - \frac {83980}{7} \, x^{14} + 9690 \, x^{13} - 6460 \, x^{12} + \frac {38760}{11} \, x^{11} - \frac {7752}{5} \, x^{10} + \frac {1615}{3} \, x^{9} - \frac {285}{2} \, x^{8} + \frac {190}{7} \, x^{7} - \frac {10}{3} \, x^{6} + \frac {1}{5} \, x^{5} \]
[In]
[Out]
Time = 0.46 (sec) , antiderivative size = 106, normalized size of antiderivative = 1.89 \[ \int (1-x)^{20} x^4 \, dx=\frac {x^{25}}{25}-\frac {5\,x^{24}}{6}+\frac {190\,x^{23}}{23}-\frac {570\,x^{22}}{11}+\frac {1615\,x^{21}}{7}-\frac {3876\,x^{20}}{5}+2040\,x^{19}-\frac {12920\,x^{18}}{3}+7410\,x^{17}-\frac {20995\,x^{16}}{2}+\frac {184756\,x^{15}}{15}-\frac {83980\,x^{14}}{7}+9690\,x^{13}-6460\,x^{12}+\frac {38760\,x^{11}}{11}-\frac {7752\,x^{10}}{5}+\frac {1615\,x^9}{3}-\frac {285\,x^8}{2}+\frac {190\,x^7}{7}-\frac {10\,x^6}{3}+\frac {x^5}{5} \]
[In]
[Out]