Optimal. Leaf size=85 \[ -\frac {(x+1)^{12}}{18 x^{18}}+\frac {(x+1)^{12}}{51 x^{17}}-\frac {5 (x+1)^{12}}{816 x^{16}}+\frac {(x+1)^{12}}{612 x^{15}}-\frac {(x+1)^{12}}{2856 x^{14}}+\frac {(x+1)^{12}}{18564 x^{13}}-\frac {(x+1)^{12}}{222768 x^{12}} \]
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Rubi [A] time = 0.02, antiderivative size = 85, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {27, 45, 37} \begin {gather*} -\frac {(x+1)^{12}}{222768 x^{12}}+\frac {(x+1)^{12}}{18564 x^{13}}-\frac {(x+1)^{12}}{2856 x^{14}}+\frac {(x+1)^{12}}{612 x^{15}}-\frac {5 (x+1)^{12}}{816 x^{16}}+\frac {(x+1)^{12}}{51 x^{17}}-\frac {(x+1)^{12}}{18 x^{18}} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 37
Rule 45
Rubi steps
\begin {align*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^{19}} \, dx &=\int \frac {(1+x)^{11}}{x^{19}} \, dx\\ &=-\frac {(1+x)^{12}}{18 x^{18}}-\frac {1}{3} \int \frac {(1+x)^{11}}{x^{18}} \, dx\\ &=-\frac {(1+x)^{12}}{18 x^{18}}+\frac {(1+x)^{12}}{51 x^{17}}+\frac {5}{51} \int \frac {(1+x)^{11}}{x^{17}} \, dx\\ &=-\frac {(1+x)^{12}}{18 x^{18}}+\frac {(1+x)^{12}}{51 x^{17}}-\frac {5 (1+x)^{12}}{816 x^{16}}-\frac {5}{204} \int \frac {(1+x)^{11}}{x^{16}} \, dx\\ &=-\frac {(1+x)^{12}}{18 x^{18}}+\frac {(1+x)^{12}}{51 x^{17}}-\frac {5 (1+x)^{12}}{816 x^{16}}+\frac {(1+x)^{12}}{612 x^{15}}+\frac {1}{204} \int \frac {(1+x)^{11}}{x^{15}} \, dx\\ &=-\frac {(1+x)^{12}}{18 x^{18}}+\frac {(1+x)^{12}}{51 x^{17}}-\frac {5 (1+x)^{12}}{816 x^{16}}+\frac {(1+x)^{12}}{612 x^{15}}-\frac {(1+x)^{12}}{2856 x^{14}}-\frac {\int \frac {(1+x)^{11}}{x^{14}} \, dx}{1428}\\ &=-\frac {(1+x)^{12}}{18 x^{18}}+\frac {(1+x)^{12}}{51 x^{17}}-\frac {5 (1+x)^{12}}{816 x^{16}}+\frac {(1+x)^{12}}{612 x^{15}}-\frac {(1+x)^{12}}{2856 x^{14}}+\frac {(1+x)^{12}}{18564 x^{13}}+\frac {\int \frac {(1+x)^{11}}{x^{13}} \, dx}{18564}\\ &=-\frac {(1+x)^{12}}{18 x^{18}}+\frac {(1+x)^{12}}{51 x^{17}}-\frac {5 (1+x)^{12}}{816 x^{16}}+\frac {(1+x)^{12}}{612 x^{15}}-\frac {(1+x)^{12}}{2856 x^{14}}+\frac {(1+x)^{12}}{18564 x^{13}}-\frac {(1+x)^{12}}{222768 x^{12}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 81, normalized size = 0.95 \begin {gather*} -\frac {1}{18 x^{18}}-\frac {11}{17 x^{17}}-\frac {55}{16 x^{16}}-\frac {11}{x^{15}}-\frac {165}{7 x^{14}}-\frac {462}{13 x^{13}}-\frac {77}{2 x^{12}}-\frac {30}{x^{11}}-\frac {33}{2 x^{10}}-\frac {55}{9 x^9}-\frac {11}{8 x^8}-\frac {1}{7 x^7} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^{19}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 60, normalized size = 0.71 \begin {gather*} -\frac {31824 \, x^{11} + 306306 \, x^{10} + 1361360 \, x^{9} + 3675672 \, x^{8} + 6683040 \, x^{7} + 8576568 \, x^{6} + 7916832 \, x^{5} + 5250960 \, x^{4} + 2450448 \, x^{3} + 765765 \, x^{2} + 144144 \, x + 12376}{222768 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 60, normalized size = 0.71 \begin {gather*} -\frac {31824 \, x^{11} + 306306 \, x^{10} + 1361360 \, x^{9} + 3675672 \, x^{8} + 6683040 \, x^{7} + 8576568 \, x^{6} + 7916832 \, x^{5} + 5250960 \, x^{4} + 2450448 \, x^{3} + 765765 \, x^{2} + 144144 \, x + 12376}{222768 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 62, normalized size = 0.73 \begin {gather*} -\frac {1}{7 x^{7}}-\frac {11}{8 x^{8}}-\frac {55}{9 x^{9}}-\frac {33}{2 x^{10}}-\frac {30}{x^{11}}-\frac {77}{2 x^{12}}-\frac {462}{13 x^{13}}-\frac {165}{7 x^{14}}-\frac {11}{x^{15}}-\frac {55}{16 x^{16}}-\frac {11}{17 x^{17}}-\frac {1}{18 x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 60, normalized size = 0.71 \begin {gather*} -\frac {31824 \, x^{11} + 306306 \, x^{10} + 1361360 \, x^{9} + 3675672 \, x^{8} + 6683040 \, x^{7} + 8576568 \, x^{6} + 7916832 \, x^{5} + 5250960 \, x^{4} + 2450448 \, x^{3} + 765765 \, x^{2} + 144144 \, x + 12376}{222768 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.06, size = 60, normalized size = 0.71 \begin {gather*} -\frac {\frac {x^{11}}{7}+\frac {11\,x^{10}}{8}+\frac {55\,x^9}{9}+\frac {33\,x^8}{2}+30\,x^7+\frac {77\,x^6}{2}+\frac {462\,x^5}{13}+\frac {165\,x^4}{7}+11\,x^3+\frac {55\,x^2}{16}+\frac {11\,x}{17}+\frac {1}{18}}{x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 61, normalized size = 0.72 \begin {gather*} \frac {- 31824 x^{11} - 306306 x^{10} - 1361360 x^{9} - 3675672 x^{8} - 6683040 x^{7} - 8576568 x^{6} - 7916832 x^{5} - 5250960 x^{4} - 2450448 x^{3} - 765765 x^{2} - 144144 x - 12376}{222768 x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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