Optimal. Leaf size=83 \[ -\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}} \]
[Out]
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Rubi [A] time = 0.0517928, antiderivative size = 83, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}} \]
Antiderivative was successfully verified.
[In] Int[((1 + x)*(1 + 2*x + x^2)^5)/x^22,x]
[Out]
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Rubi in Sympy [A] time = 11.9796, size = 80, normalized size = 0.96 \[ - \frac{1}{10 x^{10}} - \frac{1}{x^{11}} - \frac{55}{12 x^{12}} - \frac{165}{13 x^{13}} - \frac{165}{7 x^{14}} - \frac{154}{5 x^{15}} - \frac{231}{8 x^{16}} - \frac{330}{17 x^{17}} - \frac{55}{6 x^{18}} - \frac{55}{19 x^{19}} - \frac{11}{20 x^{20}} - \frac{1}{21 x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)*(x**2+2*x+1)**5/x**22,x)
[Out]
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Mathematica [A] time = 0.00684348, size = 83, normalized size = 1. \[ -\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^22,x]
[Out]
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Maple [A] time = 0.009, size = 62, normalized size = 0.8 \[ -{\frac{1}{21\,{x}^{21}}}-{\frac{11}{20\,{x}^{20}}}-{\frac{55}{19\,{x}^{19}}}-{\frac{55}{6\,{x}^{18}}}-{\frac{330}{17\,{x}^{17}}}-{\frac{231}{8\,{x}^{16}}}-{\frac{154}{5\,{x}^{15}}}-{\frac{165}{7\,{x}^{14}}}-{\frac{165}{13\,{x}^{13}}}-{\frac{55}{12\,{x}^{12}}}-{x}^{-11}-{\frac{1}{10\,{x}^{10}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)*(x^2+2*x+1)^5/x^22,x)
[Out]
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Maxima [A] time = 0.692273, size = 81, normalized size = 0.98 \[ -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^22,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.267598, size = 81, normalized size = 0.98 \[ -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^22,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.780089, size = 61, normalized size = 0.73 \[ - \frac{352716 x^{11} + 3527160 x^{10} + 16166150 x^{9} + 44767800 x^{8} + 83140200 x^{7} + 108636528 x^{6} + 101846745 x^{5} + 68468400 x^{4} + 32332300 x^{3} + 10210200 x^{2} + 1939938 x + 167960}{3527160 x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)*(x**2+2*x+1)**5/x**22,x)
[Out]
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GIAC/XCAS [A] time = 0.267445, size = 81, normalized size = 0.98 \[ -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^22,x, algorithm="giac")
[Out]