3.589 \(\int x^{10} (1+x) \left (1+2 x+x^2\right )^5 \, dx\)

Optimal. Leaf size=83 \[ \frac{x^{22}}{22}+\frac{11 x^{21}}{21}+\frac{11 x^{20}}{4}+\frac{165 x^{19}}{19}+\frac{55 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{231 x^{16}}{8}+22 x^{15}+\frac{165 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{11 x^{12}}{12}+\frac{x^{11}}{11} \]

[Out]

x^11/11 + (11*x^12)/12 + (55*x^13)/13 + (165*x^14)/14 + 22*x^15 + (231*x^16)/8 +
(462*x^17)/17 + (55*x^18)/3 + (165*x^19)/19 + (11*x^20)/4 + (11*x^21)/21 + x^22
/22

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Rubi [A]  time = 0.0635553, 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 \[ \frac{x^{22}}{22}+\frac{11 x^{21}}{21}+\frac{11 x^{20}}{4}+\frac{165 x^{19}}{19}+\frac{55 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{231 x^{16}}{8}+22 x^{15}+\frac{165 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{11 x^{12}}{12}+\frac{x^{11}}{11} \]

Antiderivative was successfully verified.

[In]  Int[x^10*(1 + x)*(1 + 2*x + x^2)^5,x]

[Out]

x^11/11 + (11*x^12)/12 + (55*x^13)/13 + (165*x^14)/14 + 22*x^15 + (231*x^16)/8 +
(462*x^17)/17 + (55*x^18)/3 + (165*x^19)/19 + (11*x^20)/4 + (11*x^21)/21 + x^22
/22

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Rubi in Sympy [A]  time = 13.0895, size = 75, normalized size = 0.9 \[ \frac{x^{22}}{22} + \frac{11 x^{21}}{21} + \frac{11 x^{20}}{4} + \frac{165 x^{19}}{19} + \frac{55 x^{18}}{3} + \frac{462 x^{17}}{17} + \frac{231 x^{16}}{8} + 22 x^{15} + \frac{165 x^{14}}{14} + \frac{55 x^{13}}{13} + \frac{11 x^{12}}{12} + \frac{x^{11}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**10*(1+x)*(x**2+2*x+1)**5,x)

[Out]

x**22/22 + 11*x**21/21 + 11*x**20/4 + 165*x**19/19 + 55*x**18/3 + 462*x**17/17 +
231*x**16/8 + 22*x**15 + 165*x**14/14 + 55*x**13/13 + 11*x**12/12 + x**11/11

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Mathematica [A]  time = 0.00282673, size = 83, normalized size = 1. \[ \frac{x^{22}}{22}+\frac{11 x^{21}}{21}+\frac{11 x^{20}}{4}+\frac{165 x^{19}}{19}+\frac{55 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{231 x^{16}}{8}+22 x^{15}+\frac{165 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{11 x^{12}}{12}+\frac{x^{11}}{11} \]

Antiderivative was successfully verified.

[In]  Integrate[x^10*(1 + x)*(1 + 2*x + x^2)^5,x]

[Out]

x^11/11 + (11*x^12)/12 + (55*x^13)/13 + (165*x^14)/14 + 22*x^15 + (231*x^16)/8 +
(462*x^17)/17 + (55*x^18)/3 + (165*x^19)/19 + (11*x^20)/4 + (11*x^21)/21 + x^22
/22

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Maple [A]  time = 0.002, size = 62, normalized size = 0.8 \[{\frac{{x}^{11}}{11}}+{\frac{11\,{x}^{12}}{12}}+{\frac{55\,{x}^{13}}{13}}+{\frac{165\,{x}^{14}}{14}}+22\,{x}^{15}+{\frac{231\,{x}^{16}}{8}}+{\frac{462\,{x}^{17}}{17}}+{\frac{55\,{x}^{18}}{3}}+{\frac{165\,{x}^{19}}{19}}+{\frac{11\,{x}^{20}}{4}}+{\frac{11\,{x}^{21}}{21}}+{\frac{{x}^{22}}{22}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^10*(1+x)*(x^2+2*x+1)^5,x)

[Out]

1/11*x^11+11/12*x^12+55/13*x^13+165/14*x^14+22*x^15+231/8*x^16+462/17*x^17+55/3*
x^18+165/19*x^19+11/4*x^20+11/21*x^21+1/22*x^22

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Maxima [A]  time = 0.696745, size = 82, normalized size = 0.99 \[ \frac{1}{22} \, x^{22} + \frac{11}{21} \, x^{21} + \frac{11}{4} \, x^{20} + \frac{165}{19} \, x^{19} + \frac{55}{3} \, x^{18} + \frac{462}{17} \, x^{17} + \frac{231}{8} \, x^{16} + 22 \, x^{15} + \frac{165}{14} \, x^{14} + \frac{55}{13} \, x^{13} + \frac{11}{12} \, x^{12} + \frac{1}{11} \, x^{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)*x^10,x, algorithm="maxima")

[Out]

1/22*x^22 + 11/21*x^21 + 11/4*x^20 + 165/19*x^19 + 55/3*x^18 + 462/17*x^17 + 231
/8*x^16 + 22*x^15 + 165/14*x^14 + 55/13*x^13 + 11/12*x^12 + 1/11*x^11

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Fricas [A]  time = 0.240601, size = 1, normalized size = 0.01 \[ \frac{1}{22} x^{22} + \frac{11}{21} x^{21} + \frac{11}{4} x^{20} + \frac{165}{19} x^{19} + \frac{55}{3} x^{18} + \frac{462}{17} x^{17} + \frac{231}{8} x^{16} + 22 x^{15} + \frac{165}{14} x^{14} + \frac{55}{13} x^{13} + \frac{11}{12} x^{12} + \frac{1}{11} x^{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)*x^10,x, algorithm="fricas")

[Out]

1/22*x^22 + 11/21*x^21 + 11/4*x^20 + 165/19*x^19 + 55/3*x^18 + 462/17*x^17 + 231
/8*x^16 + 22*x^15 + 165/14*x^14 + 55/13*x^13 + 11/12*x^12 + 1/11*x^11

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Sympy [A]  time = 0.109638, size = 75, normalized size = 0.9 \[ \frac{x^{22}}{22} + \frac{11 x^{21}}{21} + \frac{11 x^{20}}{4} + \frac{165 x^{19}}{19} + \frac{55 x^{18}}{3} + \frac{462 x^{17}}{17} + \frac{231 x^{16}}{8} + 22 x^{15} + \frac{165 x^{14}}{14} + \frac{55 x^{13}}{13} + \frac{11 x^{12}}{12} + \frac{x^{11}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**10*(1+x)*(x**2+2*x+1)**5,x)

[Out]

x**22/22 + 11*x**21/21 + 11*x**20/4 + 165*x**19/19 + 55*x**18/3 + 462*x**17/17 +
231*x**16/8 + 22*x**15 + 165*x**14/14 + 55*x**13/13 + 11*x**12/12 + x**11/11

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GIAC/XCAS [A]  time = 0.269075, size = 82, normalized size = 0.99 \[ \frac{1}{22} \, x^{22} + \frac{11}{21} \, x^{21} + \frac{11}{4} \, x^{20} + \frac{165}{19} \, x^{19} + \frac{55}{3} \, x^{18} + \frac{462}{17} \, x^{17} + \frac{231}{8} \, x^{16} + 22 \, x^{15} + \frac{165}{14} \, x^{14} + \frac{55}{13} \, x^{13} + \frac{11}{12} \, x^{12} + \frac{1}{11} \, x^{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)*x^10,x, algorithm="giac")

[Out]

1/22*x^22 + 11/21*x^21 + 11/4*x^20 + 165/19*x^19 + 55/3*x^18 + 462/17*x^17 + 231
/8*x^16 + 22*x^15 + 165/14*x^14 + 55/13*x^13 + 11/12*x^12 + 1/11*x^11