3.240 \(\int x^2 \left (a+b x^3\right )^3 \, dx\)

Optimal. Leaf size=16 \[ \frac{\left (a+b x^3\right )^4}{12 b} \]

[Out]

(a + b*x^3)^4/(12*b)

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Rubi [A]  time = 0.0118032, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\left (a+b x^3\right )^4}{12 b} \]

Antiderivative was successfully verified.

[In]  Int[x^2*(a + b*x^3)^3,x]

[Out]

(a + b*x^3)^4/(12*b)

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Rubi in Sympy [A]  time = 2.13982, size = 10, normalized size = 0.62 \[ \frac{\left (a + b x^{3}\right )^{4}}{12 b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(a + b*x**3)**4/(12*b)

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Mathematica [B]  time = 0.00303376, size = 43, normalized size = 2.69 \[ \frac{a^3 x^3}{3}+\frac{1}{2} a^2 b x^6+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{12}}{12} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2*(a + b*x^3)^3,x]

[Out]

(a^3*x^3)/3 + (a^2*b*x^6)/2 + (a*b^2*x^9)/3 + (b^3*x^12)/12

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Maple [B]  time = 0.001, size = 36, normalized size = 2.3 \[{\frac{{b}^{3}{x}^{12}}{12}}+{\frac{a{b}^{2}{x}^{9}}{3}}+{\frac{{a}^{2}b{x}^{6}}{2}}+{\frac{{a}^{3}{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(b*x^3+a)^3,x)

[Out]

1/12*b^3*x^12+1/3*a*b^2*x^9+1/2*a^2*b*x^6+1/3*a^3*x^3

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Maxima [A]  time = 1.4367, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{3} + a\right )}^{4}}{12 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/12*(b*x^3 + a)^4/b

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Fricas [A]  time = 0.190483, size = 1, normalized size = 0.06 \[ \frac{1}{12} x^{12} b^{3} + \frac{1}{3} x^{9} b^{2} a + \frac{1}{2} x^{6} b a^{2} + \frac{1}{3} x^{3} a^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/12*x^12*b^3 + 1/3*x^9*b^2*a + 1/2*x^6*b*a^2 + 1/3*x^3*a^3

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Sympy [A]  time = 0.099199, size = 36, normalized size = 2.25 \[ \frac{a^{3} x^{3}}{3} + \frac{a^{2} b x^{6}}{2} + \frac{a b^{2} x^{9}}{3} + \frac{b^{3} x^{12}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2*(b*x**3+a)**3,x)

[Out]

a**3*x**3/3 + a**2*b*x**6/2 + a*b**2*x**9/3 + b**3*x**12/12

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GIAC/XCAS [A]  time = 0.21897, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{3} + a\right )}^{4}}{12 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/12*(b*x^3 + a)^4/b