3.588 \(\int x^{11} (1+x) \left (1+2 x+x^2\right )^5 \, dx\)

Optimal. Leaf size=83 \[ \frac{x^{23}}{23}+\frac{x^{22}}{2}+\frac{55 x^{21}}{21}+\frac{33 x^{20}}{4}+\frac{330 x^{19}}{19}+\frac{77 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{165 x^{16}}{8}+11 x^{15}+\frac{55 x^{14}}{14}+\frac{11 x^{13}}{13}+\frac{x^{12}}{12} \]

[Out]

x^12/12 + (11*x^13)/13 + (55*x^14)/14 + 11*x^15 + (165*x^16)/8 + (462*x^17)/17 +
(77*x^18)/3 + (330*x^19)/19 + (33*x^20)/4 + (55*x^21)/21 + x^22/2 + x^23/23

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Rubi [A]  time = 0.0658227, 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 \[ \frac{x^{23}}{23}+\frac{x^{22}}{2}+\frac{55 x^{21}}{21}+\frac{33 x^{20}}{4}+\frac{330 x^{19}}{19}+\frac{77 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{165 x^{16}}{8}+11 x^{15}+\frac{55 x^{14}}{14}+\frac{11 x^{13}}{13}+\frac{x^{12}}{12} \]

Antiderivative was successfully verified.

[In]  Int[x^11*(1 + x)*(1 + 2*x + x^2)^5,x]

[Out]

x^12/12 + (11*x^13)/13 + (55*x^14)/14 + 11*x^15 + (165*x^16)/8 + (462*x^17)/17 +
(77*x^18)/3 + (330*x^19)/19 + (33*x^20)/4 + (55*x^21)/21 + x^22/2 + x^23/23

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Rubi in Sympy [A]  time = 13.0857, size = 73, normalized size = 0.88 \[ \frac{x^{23}}{23} + \frac{x^{22}}{2} + \frac{55 x^{21}}{21} + \frac{33 x^{20}}{4} + \frac{330 x^{19}}{19} + \frac{77 x^{18}}{3} + \frac{462 x^{17}}{17} + \frac{165 x^{16}}{8} + 11 x^{15} + \frac{55 x^{14}}{14} + \frac{11 x^{13}}{13} + \frac{x^{12}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**11*(1+x)*(x**2+2*x+1)**5,x)

[Out]

x**23/23 + x**22/2 + 55*x**21/21 + 33*x**20/4 + 330*x**19/19 + 77*x**18/3 + 462*
x**17/17 + 165*x**16/8 + 11*x**15 + 55*x**14/14 + 11*x**13/13 + x**12/12

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Mathematica [A]  time = 0.00353933, size = 83, normalized size = 1. \[ \frac{x^{23}}{23}+\frac{x^{22}}{2}+\frac{55 x^{21}}{21}+\frac{33 x^{20}}{4}+\frac{330 x^{19}}{19}+\frac{77 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{165 x^{16}}{8}+11 x^{15}+\frac{55 x^{14}}{14}+\frac{11 x^{13}}{13}+\frac{x^{12}}{12} \]

Antiderivative was successfully verified.

[In]  Integrate[x^11*(1 + x)*(1 + 2*x + x^2)^5,x]

[Out]

x^12/12 + (11*x^13)/13 + (55*x^14)/14 + 11*x^15 + (165*x^16)/8 + (462*x^17)/17 +
(77*x^18)/3 + (330*x^19)/19 + (33*x^20)/4 + (55*x^21)/21 + x^22/2 + x^23/23

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Maple [A]  time = 0.001, size = 62, normalized size = 0.8 \[{\frac{{x}^{12}}{12}}+{\frac{11\,{x}^{13}}{13}}+{\frac{55\,{x}^{14}}{14}}+11\,{x}^{15}+{\frac{165\,{x}^{16}}{8}}+{\frac{462\,{x}^{17}}{17}}+{\frac{77\,{x}^{18}}{3}}+{\frac{330\,{x}^{19}}{19}}+{\frac{33\,{x}^{20}}{4}}+{\frac{55\,{x}^{21}}{21}}+{\frac{{x}^{22}}{2}}+{\frac{{x}^{23}}{23}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^11*(1+x)*(x^2+2*x+1)^5,x)

[Out]

1/12*x^12+11/13*x^13+55/14*x^14+11*x^15+165/8*x^16+462/17*x^17+77/3*x^18+330/19*
x^19+33/4*x^20+55/21*x^21+1/2*x^22+1/23*x^23

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Maxima [A]  time = 0.688165, size = 82, normalized size = 0.99 \[ \frac{1}{23} \, x^{23} + \frac{1}{2} \, x^{22} + \frac{55}{21} \, x^{21} + \frac{33}{4} \, x^{20} + \frac{330}{19} \, x^{19} + \frac{77}{3} \, x^{18} + \frac{462}{17} \, x^{17} + \frac{165}{8} \, x^{16} + 11 \, x^{15} + \frac{55}{14} \, x^{14} + \frac{11}{13} \, x^{13} + \frac{1}{12} \, x^{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)*x^11,x, algorithm="maxima")

[Out]

1/23*x^23 + 1/2*x^22 + 55/21*x^21 + 33/4*x^20 + 330/19*x^19 + 77/3*x^18 + 462/17
*x^17 + 165/8*x^16 + 11*x^15 + 55/14*x^14 + 11/13*x^13 + 1/12*x^12

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Fricas [A]  time = 0.260544, size = 1, normalized size = 0.01 \[ \frac{1}{23} x^{23} + \frac{1}{2} x^{22} + \frac{55}{21} x^{21} + \frac{33}{4} x^{20} + \frac{330}{19} x^{19} + \frac{77}{3} x^{18} + \frac{462}{17} x^{17} + \frac{165}{8} x^{16} + 11 x^{15} + \frac{55}{14} x^{14} + \frac{11}{13} x^{13} + \frac{1}{12} x^{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)*x^11,x, algorithm="fricas")

[Out]

1/23*x^23 + 1/2*x^22 + 55/21*x^21 + 33/4*x^20 + 330/19*x^19 + 77/3*x^18 + 462/17
*x^17 + 165/8*x^16 + 11*x^15 + 55/14*x^14 + 11/13*x^13 + 1/12*x^12

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Sympy [A]  time = 0.114285, size = 73, normalized size = 0.88 \[ \frac{x^{23}}{23} + \frac{x^{22}}{2} + \frac{55 x^{21}}{21} + \frac{33 x^{20}}{4} + \frac{330 x^{19}}{19} + \frac{77 x^{18}}{3} + \frac{462 x^{17}}{17} + \frac{165 x^{16}}{8} + 11 x^{15} + \frac{55 x^{14}}{14} + \frac{11 x^{13}}{13} + \frac{x^{12}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**11*(1+x)*(x**2+2*x+1)**5,x)

[Out]

x**23/23 + x**22/2 + 55*x**21/21 + 33*x**20/4 + 330*x**19/19 + 77*x**18/3 + 462*
x**17/17 + 165*x**16/8 + 11*x**15 + 55*x**14/14 + 11*x**13/13 + x**12/12

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GIAC/XCAS [A]  time = 0.267813, size = 82, normalized size = 0.99 \[ \frac{1}{23} \, x^{23} + \frac{1}{2} \, x^{22} + \frac{55}{21} \, x^{21} + \frac{33}{4} \, x^{20} + \frac{330}{19} \, x^{19} + \frac{77}{3} \, x^{18} + \frac{462}{17} \, x^{17} + \frac{165}{8} \, x^{16} + 11 \, x^{15} + \frac{55}{14} \, x^{14} + \frac{11}{13} \, x^{13} + \frac{1}{12} \, x^{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)*x^11,x, algorithm="giac")

[Out]

1/23*x^23 + 1/2*x^22 + 55/21*x^21 + 33/4*x^20 + 330/19*x^19 + 77/3*x^18 + 462/17
*x^17 + 165/8*x^16 + 11*x^15 + 55/14*x^14 + 11/13*x^13 + 1/12*x^12