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

Optimal. Leaf size=30 \[ \frac{a^2 x^4}{4}+\frac{2}{7} a b x^7+\frac{b^2 x^{10}}{10} \]

[Out]

(a^2*x^4)/4 + (2*a*b*x^7)/7 + (b^2*x^10)/10

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Rubi [A]  time = 0.0313023, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{a^2 x^4}{4}+\frac{2}{7} a b x^7+\frac{b^2 x^{10}}{10} \]

Antiderivative was successfully verified.

[In]  Int[x^3*(a + b*x^3)^2,x]

[Out]

(a^2*x^4)/4 + (2*a*b*x^7)/7 + (b^2*x^10)/10

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Rubi in Sympy [A]  time = 5.41749, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{4}}{4} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{10}}{10} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a**2*x**4/4 + 2*a*b*x**7/7 + b**2*x**10/10

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Mathematica [A]  time = 0.00123225, size = 30, normalized size = 1. \[ \frac{a^2 x^4}{4}+\frac{2}{7} a b x^7+\frac{b^2 x^{10}}{10} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3*(a + b*x^3)^2,x]

[Out]

(a^2*x^4)/4 + (2*a*b*x^7)/7 + (b^2*x^10)/10

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Maple [A]  time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{x}^{4}{a}^{2}}{4}}+{\frac{2\,ab{x}^{7}}{7}}+{\frac{{b}^{2}{x}^{10}}{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3*(b*x^3+a)^2,x)

[Out]

1/4*x^4*a^2+2/7*a*b*x^7+1/10*b^2*x^10

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Maxima [A]  time = 1.4359, size = 32, normalized size = 1.07 \[ \frac{1}{10} \, b^{2} x^{10} + \frac{2}{7} \, a b x^{7} + \frac{1}{4} \, a^{2} x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*b^2*x^10 + 2/7*a*b*x^7 + 1/4*a^2*x^4

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Fricas [A]  time = 0.192328, size = 1, normalized size = 0.03 \[ \frac{1}{10} x^{10} b^{2} + \frac{2}{7} x^{7} b a + \frac{1}{4} x^{4} a^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*x^10*b^2 + 2/7*x^7*b*a + 1/4*x^4*a^2

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Sympy [A]  time = 0.087815, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{4}}{4} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{10}}{10} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3*(b*x**3+a)**2,x)

[Out]

a**2*x**4/4 + 2*a*b*x**7/7 + b**2*x**10/10

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GIAC/XCAS [A]  time = 0.217565, size = 32, normalized size = 1.07 \[ \frac{1}{10} \, b^{2} x^{10} + \frac{2}{7} \, a b x^{7} + \frac{1}{4} \, a^{2} x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*b^2*x^10 + 2/7*a*b*x^7 + 1/4*a^2*x^4