Optimal. Leaf size=73 \[ -\frac {(x+1)^{12}}{17 x^{17}}+\frac {5 (x+1)^{12}}{272 x^{16}}-\frac {(x+1)^{12}}{204 x^{15}}+\frac {(x+1)^{12}}{952 x^{14}}-\frac {(x+1)^{12}}{6188 x^{13}}+\frac {(x+1)^{12}}{74256 x^{12}} \]
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Rubi [A] time = 0.02, antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps used = 7, 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}}{74256 x^{12}}-\frac {(x+1)^{12}}{6188 x^{13}}+\frac {(x+1)^{12}}{952 x^{14}}-\frac {(x+1)^{12}}{204 x^{15}}+\frac {5 (x+1)^{12}}{272 x^{16}}-\frac {(x+1)^{12}}{17 x^{17}} \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^{18}} \, dx &=\int \frac {(1+x)^{11}}{x^{18}} \, dx\\ &=-\frac {(1+x)^{12}}{17 x^{17}}-\frac {5}{17} \int \frac {(1+x)^{11}}{x^{17}} \, dx\\ &=-\frac {(1+x)^{12}}{17 x^{17}}+\frac {5 (1+x)^{12}}{272 x^{16}}+\frac {5}{68} \int \frac {(1+x)^{11}}{x^{16}} \, dx\\ &=-\frac {(1+x)^{12}}{17 x^{17}}+\frac {5 (1+x)^{12}}{272 x^{16}}-\frac {(1+x)^{12}}{204 x^{15}}-\frac {1}{68} \int \frac {(1+x)^{11}}{x^{15}} \, dx\\ &=-\frac {(1+x)^{12}}{17 x^{17}}+\frac {5 (1+x)^{12}}{272 x^{16}}-\frac {(1+x)^{12}}{204 x^{15}}+\frac {(1+x)^{12}}{952 x^{14}}+\frac {1}{476} \int \frac {(1+x)^{11}}{x^{14}} \, dx\\ &=-\frac {(1+x)^{12}}{17 x^{17}}+\frac {5 (1+x)^{12}}{272 x^{16}}-\frac {(1+x)^{12}}{204 x^{15}}+\frac {(1+x)^{12}}{952 x^{14}}-\frac {(1+x)^{12}}{6188 x^{13}}-\frac {\int \frac {(1+x)^{11}}{x^{13}} \, dx}{6188}\\ &=-\frac {(1+x)^{12}}{17 x^{17}}+\frac {5 (1+x)^{12}}{272 x^{16}}-\frac {(1+x)^{12}}{204 x^{15}}+\frac {(1+x)^{12}}{952 x^{14}}-\frac {(1+x)^{12}}{6188 x^{13}}+\frac {(1+x)^{12}}{74256 x^{12}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 81, normalized size = 1.11 \begin {gather*} -\frac {1}{17 x^{17}}-\frac {11}{16 x^{16}}-\frac {11}{3 x^{15}}-\frac {165}{14 x^{14}}-\frac {330}{13 x^{13}}-\frac {77}{2 x^{12}}-\frac {42}{x^{11}}-\frac {33}{x^{10}}-\frac {55}{3 x^9}-\frac {55}{8 x^8}-\frac {11}{7 x^7}-\frac {1}{6 x^6} \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^{18}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 60, normalized size = 0.82 \begin {gather*} -\frac {12376 \, x^{11} + 116688 \, x^{10} + 510510 \, x^{9} + 1361360 \, x^{8} + 2450448 \, x^{7} + 3118752 \, x^{6} + 2858856 \, x^{5} + 1884960 \, x^{4} + 875160 \, x^{3} + 272272 \, x^{2} + 51051 \, x + 4368}{74256 \, x^{17}} \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 = 0.82 \begin {gather*} -\frac {12376 \, x^{11} + 116688 \, x^{10} + 510510 \, x^{9} + 1361360 \, x^{8} + 2450448 \, x^{7} + 3118752 \, x^{6} + 2858856 \, x^{5} + 1884960 \, x^{4} + 875160 \, x^{3} + 272272 \, x^{2} + 51051 \, x + 4368}{74256 \, x^{17}} \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 = 0.85 \begin {gather*} -\frac {1}{6 x^{6}}-\frac {11}{7 x^{7}}-\frac {55}{8 x^{8}}-\frac {55}{3 x^{9}}-\frac {33}{x^{10}}-\frac {42}{x^{11}}-\frac {77}{2 x^{12}}-\frac {330}{13 x^{13}}-\frac {165}{14 x^{14}}-\frac {11}{3 x^{15}}-\frac {11}{16 x^{16}}-\frac {1}{17 x^{17}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 60, normalized size = 0.82 \begin {gather*} -\frac {12376 \, x^{11} + 116688 \, x^{10} + 510510 \, x^{9} + 1361360 \, x^{8} + 2450448 \, x^{7} + 3118752 \, x^{6} + 2858856 \, x^{5} + 1884960 \, x^{4} + 875160 \, x^{3} + 272272 \, x^{2} + 51051 \, x + 4368}{74256 \, x^{17}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 60, normalized size = 0.82 \begin {gather*} -\frac {\frac {x^{11}}{6}+\frac {11\,x^{10}}{7}+\frac {55\,x^9}{8}+\frac {55\,x^8}{3}+33\,x^7+42\,x^6+\frac {77\,x^5}{2}+\frac {330\,x^4}{13}+\frac {165\,x^3}{14}+\frac {11\,x^2}{3}+\frac {11\,x}{16}+\frac {1}{17}}{x^{17}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 61, normalized size = 0.84 \begin {gather*} \frac {- 12376 x^{11} - 116688 x^{10} - 510510 x^{9} - 1361360 x^{8} - 2450448 x^{7} - 3118752 x^{6} - 2858856 x^{5} - 1884960 x^{4} - 875160 x^{3} - 272272 x^{2} - 51051 x - 4368}{74256 x^{17}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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