Optimal. Leaf size=61 \[ -\frac {(x+1)^{12}}{16 x^{16}}+\frac {(x+1)^{12}}{60 x^{15}}-\frac {(x+1)^{12}}{280 x^{14}}+\frac {(x+1)^{12}}{1820 x^{13}}-\frac {(x+1)^{12}}{21840 x^{12}} \]
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Rubi [A] time = 0.01, antiderivative size = 61, normalized size of antiderivative = 1.00, number of steps used = 6, 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}}{21840 x^{12}}+\frac {(x+1)^{12}}{1820 x^{13}}-\frac {(x+1)^{12}}{280 x^{14}}+\frac {(x+1)^{12}}{60 x^{15}}-\frac {(x+1)^{12}}{16 x^{16}} \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^{17}} \, dx &=\int \frac {(1+x)^{11}}{x^{17}} \, dx\\ &=-\frac {(1+x)^{12}}{16 x^{16}}-\frac {1}{4} \int \frac {(1+x)^{11}}{x^{16}} \, dx\\ &=-\frac {(1+x)^{12}}{16 x^{16}}+\frac {(1+x)^{12}}{60 x^{15}}+\frac {1}{20} \int \frac {(1+x)^{11}}{x^{15}} \, dx\\ &=-\frac {(1+x)^{12}}{16 x^{16}}+\frac {(1+x)^{12}}{60 x^{15}}-\frac {(1+x)^{12}}{280 x^{14}}-\frac {1}{140} \int \frac {(1+x)^{11}}{x^{14}} \, dx\\ &=-\frac {(1+x)^{12}}{16 x^{16}}+\frac {(1+x)^{12}}{60 x^{15}}-\frac {(1+x)^{12}}{280 x^{14}}+\frac {(1+x)^{12}}{1820 x^{13}}+\frac {\int \frac {(1+x)^{11}}{x^{13}} \, dx}{1820}\\ &=-\frac {(1+x)^{12}}{16 x^{16}}+\frac {(1+x)^{12}}{60 x^{15}}-\frac {(1+x)^{12}}{280 x^{14}}+\frac {(1+x)^{12}}{1820 x^{13}}-\frac {(1+x)^{12}}{21840 x^{12}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 83, normalized size = 1.36 \begin {gather*} -\frac {1}{16 x^{16}}-\frac {11}{15 x^{15}}-\frac {55}{14 x^{14}}-\frac {165}{13 x^{13}}-\frac {55}{2 x^{12}}-\frac {42}{x^{11}}-\frac {231}{5 x^{10}}-\frac {110}{3 x^9}-\frac {165}{8 x^8}-\frac {55}{7 x^7}-\frac {11}{6 x^6}-\frac {1}{5 x^5} \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^{17}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.40, size = 60, normalized size = 0.98 \begin {gather*} -\frac {4368 \, x^{11} + 40040 \, x^{10} + 171600 \, x^{9} + 450450 \, x^{8} + 800800 \, x^{7} + 1009008 \, x^{6} + 917280 \, x^{5} + 600600 \, x^{4} + 277200 \, x^{3} + 85800 \, x^{2} + 16016 \, x + 1365}{21840 \, x^{16}} \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 = 0.98 \begin {gather*} -\frac {4368 \, x^{11} + 40040 \, x^{10} + 171600 \, x^{9} + 450450 \, x^{8} + 800800 \, x^{7} + 1009008 \, x^{6} + 917280 \, x^{5} + 600600 \, x^{4} + 277200 \, x^{3} + 85800 \, x^{2} + 16016 \, x + 1365}{21840 \, x^{16}} \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 = 1.02 \begin {gather*} -\frac {1}{5 x^{5}}-\frac {11}{6 x^{6}}-\frac {55}{7 x^{7}}-\frac {165}{8 x^{8}}-\frac {110}{3 x^{9}}-\frac {231}{5 x^{10}}-\frac {42}{x^{11}}-\frac {55}{2 x^{12}}-\frac {165}{13 x^{13}}-\frac {55}{14 x^{14}}-\frac {11}{15 x^{15}}-\frac {1}{16 x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 60, normalized size = 0.98 \begin {gather*} -\frac {4368 \, x^{11} + 40040 \, x^{10} + 171600 \, x^{9} + 450450 \, x^{8} + 800800 \, x^{7} + 1009008 \, x^{6} + 917280 \, x^{5} + 600600 \, x^{4} + 277200 \, x^{3} + 85800 \, x^{2} + 16016 \, x + 1365}{21840 \, x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.05, size = 60, normalized size = 0.98 \begin {gather*} -\frac {\frac {x^{11}}{5}+\frac {11\,x^{10}}{6}+\frac {55\,x^9}{7}+\frac {165\,x^8}{8}+\frac {110\,x^7}{3}+\frac {231\,x^6}{5}+42\,x^5+\frac {55\,x^4}{2}+\frac {165\,x^3}{13}+\frac {55\,x^2}{14}+\frac {11\,x}{15}+\frac {1}{16}}{x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 61, normalized size = 1.00 \begin {gather*} \frac {- 4368 x^{11} - 40040 x^{10} - 171600 x^{9} - 450450 x^{8} - 800800 x^{7} - 1009008 x^{6} - 917280 x^{5} - 600600 x^{4} - 277200 x^{3} - 85800 x^{2} - 16016 x - 1365}{21840 x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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