3.142 \(\int x^2 (2+x)^5 (2+3 x) \, dx\)

Optimal. Leaf size=12 \[ \frac{1}{3} x^3 (x+2)^6 \]

[Out]

(x^3*(2 + x)^6)/3

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Rubi [A]  time = 0.00927471, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{1}{3} x^3 (x+2)^6 \]

Antiderivative was successfully verified.

[In]  Int[x^2*(2 + x)^5*(2 + 3*x),x]

[Out]

(x^3*(2 + x)^6)/3

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Rubi in Sympy [A]  time = 4.67963, size = 8, normalized size = 0.67 \[ \frac{x^{3} \left (x + 2\right )^{6}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**2*(2+x)**5*(2+3*x),x)

[Out]

x**3*(x + 2)**6/3

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Mathematica [B]  time = 0.00306096, size = 42, normalized size = 3.5 \[ \frac{x^9}{3}+4 x^8+20 x^7+\frac{160 x^6}{3}+80 x^5+64 x^4+\frac{64 x^3}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2*(2 + x)^5*(2 + 3*x),x]

[Out]

(64*x^3)/3 + 64*x^4 + 80*x^5 + (160*x^6)/3 + 20*x^7 + 4*x^8 + x^9/3

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Maple [B]  time = 0.002, size = 37, normalized size = 3.1 \[{\frac{{x}^{9}}{3}}+4\,{x}^{8}+20\,{x}^{7}+{\frac{160\,{x}^{6}}{3}}+80\,{x}^{5}+64\,{x}^{4}+{\frac{64\,{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(2+x)^5*(2+3*x),x)

[Out]

1/3*x^9+4*x^8+20*x^7+160/3*x^6+80*x^5+64*x^4+64/3*x^3

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Maxima [A]  time = 1.3504, size = 49, normalized size = 4.08 \[ \frac{1}{3} \, x^{9} + 4 \, x^{8} + 20 \, x^{7} + \frac{160}{3} \, x^{6} + 80 \, x^{5} + 64 \, x^{4} + \frac{64}{3} \, x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)*(x + 2)^5*x^2,x, algorithm="maxima")

[Out]

1/3*x^9 + 4*x^8 + 20*x^7 + 160/3*x^6 + 80*x^5 + 64*x^4 + 64/3*x^3

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Fricas [A]  time = 0.175227, size = 1, normalized size = 0.08 \[ \frac{1}{3} x^{9} + 4 x^{8} + 20 x^{7} + \frac{160}{3} x^{6} + 80 x^{5} + 64 x^{4} + \frac{64}{3} x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)*(x + 2)^5*x^2,x, algorithm="fricas")

[Out]

1/3*x^9 + 4*x^8 + 20*x^7 + 160/3*x^6 + 80*x^5 + 64*x^4 + 64/3*x^3

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Sympy [A]  time = 0.104304, size = 37, normalized size = 3.08 \[ \frac{x^{9}}{3} + 4 x^{8} + 20 x^{7} + \frac{160 x^{6}}{3} + 80 x^{5} + 64 x^{4} + \frac{64 x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2*(2+x)**5*(2+3*x),x)

[Out]

x**9/3 + 4*x**8 + 20*x**7 + 160*x**6/3 + 80*x**5 + 64*x**4 + 64*x**3/3

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GIAC/XCAS [A]  time = 0.280048, size = 49, normalized size = 4.08 \[ \frac{1}{3} \, x^{9} + 4 \, x^{8} + 20 \, x^{7} + \frac{160}{3} \, x^{6} + 80 \, x^{5} + 64 \, x^{4} + \frac{64}{3} \, x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)*(x + 2)^5*x^2,x, algorithm="giac")

[Out]

1/3*x^9 + 4*x^8 + 20*x^7 + 160/3*x^6 + 80*x^5 + 64*x^4 + 64/3*x^3