Optimal. Leaf size=80 \[ \frac{x^{22}}{22}+\frac{11 x^{20}}{20}+\frac{55 x^{18}}{18}+\frac{165 x^{16}}{16}+\frac{165 x^{14}}{7}+\frac{77 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{165 x^8}{4}+\frac{55 x^6}{2}+\frac{55 x^4}{4}+\frac{11 x^2}{2}+\log (x) \]
[Out]
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Rubi [A] time = 0.0614809, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{x^{22}}{22}+\frac{11 x^{20}}{20}+\frac{55 x^{18}}{18}+\frac{165 x^{16}}{16}+\frac{165 x^{14}}{7}+\frac{77 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{165 x^8}{4}+\frac{55 x^6}{2}+\frac{55 x^4}{4}+\frac{11 x^2}{2}+\log (x) \]
Antiderivative was successfully verified.
[In] Int[((1 + x^2)*(1 + 2*x^2 + x^4)^5)/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{22}}{22} + \frac{11 x^{20}}{20} + \frac{55 x^{18}}{18} + \frac{165 x^{16}}{16} + \frac{165 x^{14}}{7} + \frac{77 x^{12}}{2} + \frac{231 x^{10}}{5} + \frac{165 x^{8}}{4} + \frac{55 x^{6}}{2} + \frac{11 x^{2}}{2} + \frac{\log{\left (x^{2} \right )}}{2} + \frac{55 \int ^{x^{2}} x\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+1)*(x**4+2*x**2+1)**5/x,x)
[Out]
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Mathematica [A] time = 0.00520964, size = 80, normalized size = 1. \[ \frac{x^{22}}{22}+\frac{11 x^{20}}{20}+\frac{55 x^{18}}{18}+\frac{165 x^{16}}{16}+\frac{165 x^{14}}{7}+\frac{77 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{165 x^8}{4}+\frac{55 x^6}{2}+\frac{55 x^4}{4}+\frac{11 x^2}{2}+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[((1 + x^2)*(1 + 2*x^2 + x^4)^5)/x,x]
[Out]
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Maple [A] time = 0.004, size = 59, normalized size = 0.7 \[{\frac{11\,{x}^{2}}{2}}+{\frac{55\,{x}^{4}}{4}}+{\frac{55\,{x}^{6}}{2}}+{\frac{165\,{x}^{8}}{4}}+{\frac{231\,{x}^{10}}{5}}+{\frac{77\,{x}^{12}}{2}}+{\frac{165\,{x}^{14}}{7}}+{\frac{165\,{x}^{16}}{16}}+{\frac{55\,{x}^{18}}{18}}+{\frac{11\,{x}^{20}}{20}}+{\frac{{x}^{22}}{22}}+\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+1)*(x^4+2*x^2+1)^5/x,x)
[Out]
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Maxima [A] time = 0.698766, size = 84, normalized size = 1.05 \[ \frac{1}{22} \, x^{22} + \frac{11}{20} \, x^{20} + \frac{55}{18} \, x^{18} + \frac{165}{16} \, x^{16} + \frac{165}{7} \, x^{14} + \frac{77}{2} \, x^{12} + \frac{231}{5} \, x^{10} + \frac{165}{4} \, x^{8} + \frac{55}{2} \, x^{6} + \frac{55}{4} \, x^{4} + \frac{11}{2} \, x^{2} + \frac{1}{2} \, \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 2*x^2 + 1)^5*(x^2 + 1)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.249745, size = 78, normalized size = 0.98 \[ \frac{1}{22} \, x^{22} + \frac{11}{20} \, x^{20} + \frac{55}{18} \, x^{18} + \frac{165}{16} \, x^{16} + \frac{165}{7} \, x^{14} + \frac{77}{2} \, x^{12} + \frac{231}{5} \, x^{10} + \frac{165}{4} \, x^{8} + \frac{55}{2} \, x^{6} + \frac{55}{4} \, x^{4} + \frac{11}{2} \, x^{2} + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 2*x^2 + 1)^5*(x^2 + 1)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.204824, size = 75, normalized size = 0.94 \[ \frac{x^{22}}{22} + \frac{11 x^{20}}{20} + \frac{55 x^{18}}{18} + \frac{165 x^{16}}{16} + \frac{165 x^{14}}{7} + \frac{77 x^{12}}{2} + \frac{231 x^{10}}{5} + \frac{165 x^{8}}{4} + \frac{55 x^{6}}{2} + \frac{55 x^{4}}{4} + \frac{11 x^{2}}{2} + \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+1)*(x**4+2*x**2+1)**5/x,x)
[Out]
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GIAC/XCAS [A] time = 0.262361, size = 84, normalized size = 1.05 \[ \frac{1}{22} \, x^{22} + \frac{11}{20} \, x^{20} + \frac{55}{18} \, x^{18} + \frac{165}{16} \, x^{16} + \frac{165}{7} \, x^{14} + \frac{77}{2} \, x^{12} + \frac{231}{5} \, x^{10} + \frac{165}{4} \, x^{8} + \frac{55}{2} \, x^{6} + \frac{55}{4} \, x^{4} + \frac{11}{2} \, x^{2} + \frac{1}{2} \,{\rm ln}\left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 2*x^2 + 1)^5*(x^2 + 1)/x,x, algorithm="giac")
[Out]