Optimal. Leaf size=80 \[ \frac {x^{22}}{22}+\frac {11 x^{20}}{20}+\frac {55 x^{18}}{18}+\frac {165 x^{16}}{16}+\frac {165 x^{14}}{7}+\frac {77 x^{12}}{2}+\frac {231 x^{10}}{5}+\frac {165 x^8}{4}+\frac {55 x^6}{2}+\frac {55 x^4}{4}+\frac {11 x^2}{2}+\log (x) \]
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Rubi [A] time = 0.03, antiderivative size = 80, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {28, 266, 43} \[ \frac {x^{22}}{22}+\frac {11 x^{20}}{20}+\frac {55 x^{18}}{18}+\frac {165 x^{16}}{16}+\frac {165 x^{14}}{7}+\frac {77 x^{12}}{2}+\frac {231 x^{10}}{5}+\frac {165 x^8}{4}+\frac {55 x^6}{2}+\frac {55 x^4}{4}+\frac {11 x^2}{2}+\log (x) \]
Antiderivative was successfully verified.
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Rule 28
Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (1+x^2\right ) \left (1+2 x^2+x^4\right )^5}{x} \, dx &=\int \frac {\left (1+x^2\right )^{11}}{x} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(1+x)^{11}}{x} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (11+\frac {1}{x}+55 x+165 x^2+330 x^3+462 x^4+462 x^5+330 x^6+165 x^7+55 x^8+11 x^9+x^{10}\right ) \, dx,x,x^2\right )\\ &=\frac {11 x^2}{2}+\frac {55 x^4}{4}+\frac {55 x^6}{2}+\frac {165 x^8}{4}+\frac {231 x^{10}}{5}+\frac {77 x^{12}}{2}+\frac {165 x^{14}}{7}+\frac {165 x^{16}}{16}+\frac {55 x^{18}}{18}+\frac {11 x^{20}}{20}+\frac {x^{22}}{22}+\log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 80, normalized size = 1.00 \[ \frac {x^{22}}{22}+\frac {11 x^{20}}{20}+\frac {55 x^{18}}{18}+\frac {165 x^{16}}{16}+\frac {165 x^{14}}{7}+\frac {77 x^{12}}{2}+\frac {231 x^{10}}{5}+\frac {165 x^8}{4}+\frac {55 x^6}{2}+\frac {55 x^4}{4}+\frac {11 x^2}{2}+\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 58, normalized size = 0.72 \[ \frac {1}{22} \, x^{22} + \frac {11}{20} \, x^{20} + \frac {55}{18} \, x^{18} + \frac {165}{16} \, x^{16} + \frac {165}{7} \, x^{14} + \frac {77}{2} \, x^{12} + \frac {231}{5} \, x^{10} + \frac {165}{4} \, x^{8} + \frac {55}{2} \, x^{6} + \frac {55}{4} \, x^{4} + \frac {11}{2} \, x^{2} + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 62, normalized size = 0.78 \[ \frac {1}{22} \, x^{22} + \frac {11}{20} \, x^{20} + \frac {55}{18} \, x^{18} + \frac {165}{16} \, x^{16} + \frac {165}{7} \, x^{14} + \frac {77}{2} \, x^{12} + \frac {231}{5} \, x^{10} + \frac {165}{4} \, x^{8} + \frac {55}{2} \, x^{6} + \frac {55}{4} \, x^{4} + \frac {11}{2} \, x^{2} + \frac {1}{2} \, \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 59, normalized size = 0.74 \[ \frac {x^{22}}{22}+\frac {11 x^{20}}{20}+\frac {55 x^{18}}{18}+\frac {165 x^{16}}{16}+\frac {165 x^{14}}{7}+\frac {77 x^{12}}{2}+\frac {231 x^{10}}{5}+\frac {165 x^{8}}{4}+\frac {55 x^{6}}{2}+\frac {55 x^{4}}{4}+\frac {11 x^{2}}{2}+\ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.82, size = 62, normalized size = 0.78 \[ \frac {1}{22} \, x^{22} + \frac {11}{20} \, x^{20} + \frac {55}{18} \, x^{18} + \frac {165}{16} \, x^{16} + \frac {165}{7} \, x^{14} + \frac {77}{2} \, x^{12} + \frac {231}{5} \, x^{10} + \frac {165}{4} \, x^{8} + \frac {55}{2} \, x^{6} + \frac {55}{4} \, x^{4} + \frac {11}{2} \, x^{2} + \frac {1}{2} \, \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 58, normalized size = 0.72 \[ \ln \relax (x)+\frac {11\,x^2}{2}+\frac {55\,x^4}{4}+\frac {55\,x^6}{2}+\frac {165\,x^8}{4}+\frac {231\,x^{10}}{5}+\frac {77\,x^{12}}{2}+\frac {165\,x^{14}}{7}+\frac {165\,x^{16}}{16}+\frac {55\,x^{18}}{18}+\frac {11\,x^{20}}{20}+\frac {x^{22}}{22} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 75, normalized size = 0.94 \[ \frac {x^{22}}{22} + \frac {11 x^{20}}{20} + \frac {55 x^{18}}{18} + \frac {165 x^{16}}{16} + \frac {165 x^{14}}{7} + \frac {77 x^{12}}{2} + \frac {231 x^{10}}{5} + \frac {165 x^{8}}{4} + \frac {55 x^{6}}{2} + \frac {55 x^{4}}{4} + \frac {11 x^{2}}{2} + \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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