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

Optimal. Leaf size=9 \[ \frac{1}{12} (x+1)^{12} \]

[Out]

(1 + x)^12/12

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Rubi [A]  time = 0.00537059, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{1}{12} (x+1)^{12} \]

Antiderivative was successfully verified.

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

[Out]

(1 + x)^12/12

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Rubi in Sympy [A]  time = 3.88044, size = 5, normalized size = 0.56 \[ \frac{\left (x + 1\right )^{12}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(x + 1)**12/12

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Mathematica [A]  time = 0.00206837, size = 9, normalized size = 1. \[ \frac{1}{12} (x+1)^{12} \]

Antiderivative was successfully verified.

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

[Out]

(1 + x)^12/12

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Maple [B]  time = 0.002, size = 56, normalized size = 6.2 \[{\frac{{x}^{12}}{12}}+{x}^{11}+{\frac{11\,{x}^{10}}{2}}+{\frac{55\,{x}^{9}}{3}}+{\frac{165\,{x}^{8}}{4}}+66\,{x}^{7}+77\,{x}^{6}+66\,{x}^{5}+{\frac{165\,{x}^{4}}{4}}+{\frac{55\,{x}^{3}}{3}}+{\frac{11\,{x}^{2}}{2}}+x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1+x)*(x^2+2*x+1)^5,x)

[Out]

1/12*x^12+x^11+11/2*x^10+55/3*x^9+165/4*x^8+66*x^7+77*x^6+66*x^5+165/4*x^4+55/3*
x^3+11/2*x^2+x

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Maxima [A]  time = 0.695951, size = 16, normalized size = 1.78 \[ \frac{1}{12} \,{\left (x^{2} + 2 \, x + 1\right )}^{6} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/12*(x^2 + 2*x + 1)^6

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Fricas [A]  time = 0.273152, size = 1, normalized size = 0.11 \[ \frac{1}{12} x^{12} + x^{11} + \frac{11}{2} x^{10} + \frac{55}{3} x^{9} + \frac{165}{4} x^{8} + 66 x^{7} + 77 x^{6} + 66 x^{5} + \frac{165}{4} x^{4} + \frac{55}{3} x^{3} + \frac{11}{2} x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/12*x^12 + x^11 + 11/2*x^10 + 55/3*x^9 + 165/4*x^8 + 66*x^7 + 77*x^6 + 66*x^5 +
165/4*x^4 + 55/3*x^3 + 11/2*x^2 + x

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Sympy [A]  time = 0.134753, size = 65, normalized size = 7.22 \[ \frac{x^{12}}{12} + x^{11} + \frac{11 x^{10}}{2} + \frac{55 x^{9}}{3} + \frac{165 x^{8}}{4} + 66 x^{7} + 77 x^{6} + 66 x^{5} + \frac{165 x^{4}}{4} + \frac{55 x^{3}}{3} + \frac{11 x^{2}}{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**12/12 + x**11 + 11*x**10/2 + 55*x**9/3 + 165*x**8/4 + 66*x**7 + 77*x**6 + 66*
x**5 + 165*x**4/4 + 55*x**3/3 + 11*x**2/2 + x

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GIAC/XCAS [A]  time = 0.266488, size = 74, normalized size = 8.22 \[ \frac{1}{12} \, x^{12} + x^{11} + \frac{11}{2} \, x^{10} + \frac{55}{3} \, x^{9} + \frac{165}{4} \, x^{8} + 66 \, x^{7} + 77 \, x^{6} + 66 \, x^{5} + \frac{165}{4} \, x^{4} + \frac{55}{3} \, x^{3} + \frac{11}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/12*x^12 + x^11 + 11/2*x^10 + 55/3*x^9 + 165/4*x^8 + 66*x^7 + 77*x^6 + 66*x^5 +
165/4*x^4 + 55/3*x^3 + 11/2*x^2 + x