3.597 \(\int x^2 (1+x) \left (1+2 x+x^2\right )^5 \, dx\)

Optimal. Leaf size=28 \[ \frac{1}{14} (x+1)^{14}-\frac{2}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12} \]

[Out]

(1 + x)^12/12 - (2*(1 + x)^13)/13 + (1 + x)^14/14

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Rubi [A]  time = 0.0377602, antiderivative size = 28, 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 \[ \frac{1}{14} (x+1)^{14}-\frac{2}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12} \]

Antiderivative was successfully verified.

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

[Out]

(1 + x)^12/12 - (2*(1 + x)^13)/13 + (1 + x)^14/14

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Rubi in Sympy [A]  time = 9.57769, size = 20, normalized size = 0.71 \[ \frac{\left (x + 1\right )^{14}}{14} - \frac{2 \left (x + 1\right )^{13}}{13} + \frac{\left (x + 1\right )^{12}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(x + 1)**14/14 - 2*(x + 1)**13/13 + (x + 1)**12/12

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Mathematica [B]  time = 0.00268914, size = 79, normalized size = 2.82 \[ \frac{x^{14}}{14}+\frac{11 x^{13}}{13}+\frac{55 x^{12}}{12}+15 x^{11}+33 x^{10}+\frac{154 x^9}{3}+\frac{231 x^8}{4}+\frac{330 x^7}{7}+\frac{55 x^6}{2}+11 x^5+\frac{11 x^4}{4}+\frac{x^3}{3} \]

Antiderivative was successfully verified.

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

[Out]

x^3/3 + (11*x^4)/4 + 11*x^5 + (55*x^6)/2 + (330*x^7)/7 + (231*x^8)/4 + (154*x^9)
/3 + 33*x^10 + 15*x^11 + (55*x^12)/12 + (11*x^13)/13 + x^14/14

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Maple [B]  time = 0.002, size = 62, normalized size = 2.2 \[{\frac{{x}^{14}}{14}}+{\frac{11\,{x}^{13}}{13}}+{\frac{55\,{x}^{12}}{12}}+15\,{x}^{11}+33\,{x}^{10}+{\frac{154\,{x}^{9}}{3}}+{\frac{231\,{x}^{8}}{4}}+{\frac{330\,{x}^{7}}{7}}+{\frac{55\,{x}^{6}}{2}}+11\,{x}^{5}+{\frac{11\,{x}^{4}}{4}}+{\frac{{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(1+x)*(x^2+2*x+1)^5,x)

[Out]

1/14*x^14+11/13*x^13+55/12*x^12+15*x^11+33*x^10+154/3*x^9+231/4*x^8+330/7*x^7+55
/2*x^6+11*x^5+11/4*x^4+1/3*x^3

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Maxima [A]  time = 0.689096, size = 82, normalized size = 2.93 \[ \frac{1}{14} \, x^{14} + \frac{11}{13} \, x^{13} + \frac{55}{12} \, x^{12} + 15 \, x^{11} + 33 \, x^{10} + \frac{154}{3} \, x^{9} + \frac{231}{4} \, x^{8} + \frac{330}{7} \, x^{7} + \frac{55}{2} \, x^{6} + 11 \, x^{5} + \frac{11}{4} \, x^{4} + \frac{1}{3} \, x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/14*x^14 + 11/13*x^13 + 55/12*x^12 + 15*x^11 + 33*x^10 + 154/3*x^9 + 231/4*x^8
+ 330/7*x^7 + 55/2*x^6 + 11*x^5 + 11/4*x^4 + 1/3*x^3

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Fricas [A]  time = 0.244273, size = 1, normalized size = 0.04 \[ \frac{1}{14} x^{14} + \frac{11}{13} x^{13} + \frac{55}{12} x^{12} + 15 x^{11} + 33 x^{10} + \frac{154}{3} x^{9} + \frac{231}{4} x^{8} + \frac{330}{7} x^{7} + \frac{55}{2} x^{6} + 11 x^{5} + \frac{11}{4} x^{4} + \frac{1}{3} x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/14*x^14 + 11/13*x^13 + 55/12*x^12 + 15*x^11 + 33*x^10 + 154/3*x^9 + 231/4*x^8
+ 330/7*x^7 + 55/2*x^6 + 11*x^5 + 11/4*x^4 + 1/3*x^3

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Sympy [A]  time = 0.107065, size = 71, normalized size = 2.54 \[ \frac{x^{14}}{14} + \frac{11 x^{13}}{13} + \frac{55 x^{12}}{12} + 15 x^{11} + 33 x^{10} + \frac{154 x^{9}}{3} + \frac{231 x^{8}}{4} + \frac{330 x^{7}}{7} + \frac{55 x^{6}}{2} + 11 x^{5} + \frac{11 x^{4}}{4} + \frac{x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**14/14 + 11*x**13/13 + 55*x**12/12 + 15*x**11 + 33*x**10 + 154*x**9/3 + 231*x*
*8/4 + 330*x**7/7 + 55*x**6/2 + 11*x**5 + 11*x**4/4 + x**3/3

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GIAC/XCAS [A]  time = 0.266329, size = 82, normalized size = 2.93 \[ \frac{1}{14} \, x^{14} + \frac{11}{13} \, x^{13} + \frac{55}{12} \, x^{12} + 15 \, x^{11} + 33 \, x^{10} + \frac{154}{3} \, x^{9} + \frac{231}{4} \, x^{8} + \frac{330}{7} \, x^{7} + \frac{55}{2} \, x^{6} + 11 \, x^{5} + \frac{11}{4} \, x^{4} + \frac{1}{3} \, x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/14*x^14 + 11/13*x^13 + 55/12*x^12 + 15*x^11 + 33*x^10 + 154/3*x^9 + 231/4*x^8
+ 330/7*x^7 + 55/2*x^6 + 11*x^5 + 11/4*x^4 + 1/3*x^3