Optimal. Leaf size=97 \[ -\frac{(x+1)^{12}}{19 x^{19}}+\frac{7 (x+1)^{12}}{342 x^{18}}-\frac{7 (x+1)^{12}}{969 x^{17}}+\frac{35 (x+1)^{12}}{15504 x^{16}}-\frac{7 (x+1)^{12}}{11628 x^{15}}+\frac{(x+1)^{12}}{7752 x^{14}}-\frac{(x+1)^{12}}{50388 x^{13}}+\frac{(x+1)^{12}}{604656 x^{12}} \]
[Out]
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Rubi [A] time = 0.0760497, antiderivative size = 97, normalized size of antiderivative = 1., number of steps used = 9, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ -\frac{(x+1)^{12}}{19 x^{19}}+\frac{7 (x+1)^{12}}{342 x^{18}}-\frac{7 (x+1)^{12}}{969 x^{17}}+\frac{35 (x+1)^{12}}{15504 x^{16}}-\frac{7 (x+1)^{12}}{11628 x^{15}}+\frac{(x+1)^{12}}{7752 x^{14}}-\frac{(x+1)^{12}}{50388 x^{13}}+\frac{(x+1)^{12}}{604656 x^{12}} \]
Antiderivative was successfully verified.
[In] Int[((1 + x)*(1 + 2*x + x^2)^5)/x^20,x]
[Out]
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Rubi in Sympy [A] time = 11.9082, size = 76, normalized size = 0.78 \[ - \frac{1}{8 x^{8}} - \frac{11}{9 x^{9}} - \frac{11}{2 x^{10}} - \frac{15}{x^{11}} - \frac{55}{2 x^{12}} - \frac{462}{13 x^{13}} - \frac{33}{x^{14}} - \frac{22}{x^{15}} - \frac{165}{16 x^{16}} - \frac{55}{17 x^{17}} - \frac{11}{18 x^{18}} - \frac{1}{19 x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)*(x**2+2*x+1)**5/x**20,x)
[Out]
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Mathematica [A] time = 0.00409546, size = 79, normalized size = 0.81 \[ -\frac{1}{19 x^{19}}-\frac{11}{18 x^{18}}-\frac{55}{17 x^{17}}-\frac{165}{16 x^{16}}-\frac{22}{x^{15}}-\frac{33}{x^{14}}-\frac{462}{13 x^{13}}-\frac{55}{2 x^{12}}-\frac{15}{x^{11}}-\frac{11}{2 x^{10}}-\frac{11}{9 x^9}-\frac{1}{8 x^8} \]
Antiderivative was successfully verified.
[In] Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^20,x]
[Out]
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Maple [A] time = 0.009, size = 62, normalized size = 0.6 \[ -{\frac{55}{2\,{x}^{12}}}-22\,{x}^{-15}-{\frac{165}{16\,{x}^{16}}}-{\frac{1}{19\,{x}^{19}}}-{\frac{462}{13\,{x}^{13}}}-{\frac{11}{2\,{x}^{10}}}-{\frac{55}{17\,{x}^{17}}}-{\frac{1}{8\,{x}^{8}}}-15\,{x}^{-11}-33\,{x}^{-14}-{\frac{11}{9\,{x}^{9}}}-{\frac{11}{18\,{x}^{18}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)*(x^2+2*x+1)^5/x^20,x)
[Out]
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Maxima [A] time = 0.683687, size = 81, normalized size = 0.84 \[ -\frac{75582 \, x^{11} + 739024 \, x^{10} + 3325608 \, x^{9} + 9069840 \, x^{8} + 16628040 \, x^{7} + 21488544 \, x^{6} + 19953648 \, x^{5} + 13302432 \, x^{4} + 6235515 \, x^{3} + 1956240 \, x^{2} + 369512 \, x + 31824}{604656 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^20,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269404, size = 81, normalized size = 0.84 \[ -\frac{75582 \, x^{11} + 739024 \, x^{10} + 3325608 \, x^{9} + 9069840 \, x^{8} + 16628040 \, x^{7} + 21488544 \, x^{6} + 19953648 \, x^{5} + 13302432 \, x^{4} + 6235515 \, x^{3} + 1956240 \, x^{2} + 369512 \, x + 31824}{604656 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^20,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.712628, size = 61, normalized size = 0.63 \[ - \frac{75582 x^{11} + 739024 x^{10} + 3325608 x^{9} + 9069840 x^{8} + 16628040 x^{7} + 21488544 x^{6} + 19953648 x^{5} + 13302432 x^{4} + 6235515 x^{3} + 1956240 x^{2} + 369512 x + 31824}{604656 x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)*(x**2+2*x+1)**5/x**20,x)
[Out]
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GIAC/XCAS [A] time = 0.271124, size = 81, normalized size = 0.84 \[ -\frac{75582 \, x^{11} + 739024 \, x^{10} + 3325608 \, x^{9} + 9069840 \, x^{8} + 16628040 \, x^{7} + 21488544 \, x^{6} + 19953648 \, x^{5} + 13302432 \, x^{4} + 6235515 \, x^{3} + 1956240 \, x^{2} + 369512 \, x + 31824}{604656 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^20,x, algorithm="giac")
[Out]