3.70 \(\int x \left (1+x^2\right ) \left (1+2 x^2+x^4\right )^5 \, dx\)

Optimal. Leaf size=11 \[ \frac{1}{24} \left (x^2+1\right )^{12} \]

[Out]

(1 + x^2)^12/24

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Rubi [A]  time = 0.00867986, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{1}{24} \left (x^2+1\right )^{12} \]

Antiderivative was successfully verified.

[In]  Int[x*(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]

[Out]

(1 + x^2)^12/24

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Rubi in Sympy [A]  time = 3.54478, size = 7, normalized size = 0.64 \[ \frac{\left (x^{2} + 1\right )^{12}}{24} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*(x**2+1)*(x**4+2*x**2+1)**5,x)

[Out]

(x**2 + 1)**12/24

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Mathematica [A]  time = 0.00245139, size = 11, normalized size = 1. \[ \frac{1}{24} \left (x^2+1\right )^{12} \]

Antiderivative was successfully verified.

[In]  Integrate[x*(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]

[Out]

(1 + x^2)^12/24

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Maple [B]  time = 0.002, size = 62, normalized size = 5.6 \[{\frac{{x}^{24}}{24}}+{\frac{{x}^{22}}{2}}+{\frac{11\,{x}^{20}}{4}}+{\frac{55\,{x}^{18}}{6}}+{\frac{165\,{x}^{16}}{8}}+33\,{x}^{14}+{\frac{77\,{x}^{12}}{2}}+33\,{x}^{10}+{\frac{165\,{x}^{8}}{8}}+{\frac{55\,{x}^{6}}{6}}+{\frac{11\,{x}^{4}}{4}}+{\frac{{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(x^2+1)*(x^4+2*x^2+1)^5,x)

[Out]

1/24*x^24+1/2*x^22+11/4*x^20+55/6*x^18+165/8*x^16+33*x^14+77/2*x^12+33*x^10+165/
8*x^8+55/6*x^6+11/4*x^4+1/2*x^2

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Maxima [A]  time = 0.699148, size = 82, normalized size = 7.45 \[ \frac{1}{24} \, x^{24} + \frac{1}{2} \, x^{22} + \frac{11}{4} \, x^{20} + \frac{55}{6} \, x^{18} + \frac{165}{8} \, x^{16} + 33 \, x^{14} + \frac{77}{2} \, x^{12} + 33 \, x^{10} + \frac{165}{8} \, x^{8} + \frac{55}{6} \, x^{6} + \frac{11}{4} \, x^{4} + \frac{1}{2} \, x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 + 2*x^2 + 1)^5*(x^2 + 1)*x,x, algorithm="maxima")

[Out]

1/24*x^24 + 1/2*x^22 + 11/4*x^20 + 55/6*x^18 + 165/8*x^16 + 33*x^14 + 77/2*x^12
+ 33*x^10 + 165/8*x^8 + 55/6*x^6 + 11/4*x^4 + 1/2*x^2

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Fricas [A]  time = 0.229068, size = 1, normalized size = 0.09 \[ \frac{1}{24} x^{24} + \frac{1}{2} x^{22} + \frac{11}{4} x^{20} + \frac{55}{6} x^{18} + \frac{165}{8} x^{16} + 33 x^{14} + \frac{77}{2} x^{12} + 33 x^{10} + \frac{165}{8} x^{8} + \frac{55}{6} x^{6} + \frac{11}{4} x^{4} + \frac{1}{2} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 + 2*x^2 + 1)^5*(x^2 + 1)*x,x, algorithm="fricas")

[Out]

1/24*x^24 + 1/2*x^22 + 11/4*x^20 + 55/6*x^18 + 165/8*x^16 + 33*x^14 + 77/2*x^12
+ 33*x^10 + 165/8*x^8 + 55/6*x^6 + 11/4*x^4 + 1/2*x^2

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Sympy [A]  time = 0.107175, size = 71, normalized size = 6.45 \[ \frac{x^{24}}{24} + \frac{x^{22}}{2} + \frac{11 x^{20}}{4} + \frac{55 x^{18}}{6} + \frac{165 x^{16}}{8} + 33 x^{14} + \frac{77 x^{12}}{2} + 33 x^{10} + \frac{165 x^{8}}{8} + \frac{55 x^{6}}{6} + \frac{11 x^{4}}{4} + \frac{x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(x**2+1)*(x**4+2*x**2+1)**5,x)

[Out]

x**24/24 + x**22/2 + 11*x**20/4 + 55*x**18/6 + 165*x**16/8 + 33*x**14 + 77*x**12
/2 + 33*x**10 + 165*x**8/8 + 55*x**6/6 + 11*x**4/4 + x**2/2

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GIAC/XCAS [A]  time = 0.261091, size = 82, normalized size = 7.45 \[ \frac{1}{24} \, x^{24} + \frac{1}{2} \, x^{22} + \frac{11}{4} \, x^{20} + \frac{55}{6} \, x^{18} + \frac{165}{8} \, x^{16} + 33 \, x^{14} + \frac{77}{2} \, x^{12} + 33 \, x^{10} + \frac{165}{8} \, x^{8} + \frac{55}{6} \, x^{6} + \frac{11}{4} \, x^{4} + \frac{1}{2} \, x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 + 2*x^2 + 1)^5*(x^2 + 1)*x,x, algorithm="giac")

[Out]

1/24*x^24 + 1/2*x^22 + 11/4*x^20 + 55/6*x^18 + 165/8*x^16 + 33*x^14 + 77/2*x^12
+ 33*x^10 + 165/8*x^8 + 55/6*x^6 + 11/4*x^4 + 1/2*x^2