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

Optimal. Leaf size=30 \[ \frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9} \]

[Out]

(a^2*x^7)/7 + (a*b*x^8)/4 + (b^2*x^9)/9

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Rubi [A]  time = 0.0557625, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9} \]

Antiderivative was successfully verified.

[In]  Int[x^2*(a*x^2 + b*x^3)^2,x]

[Out]

(a^2*x^7)/7 + (a*b*x^8)/4 + (b^2*x^9)/9

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Rubi in Sympy [A]  time = 8.06149, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{7}}{7} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{9}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a**2*x**7/7 + a*b*x**8/4 + b**2*x**9/9

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Mathematica [A]  time = 0.0026613, size = 30, normalized size = 1. \[ \frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9} \]

Antiderivative was successfully verified.

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

[Out]

(a^2*x^7)/7 + (a*b*x^8)/4 + (b^2*x^9)/9

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Maple [A]  time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{7}}{7}}+{\frac{ab{x}^{8}}{4}}+{\frac{{b}^{2}{x}^{9}}{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(b*x^3+a*x^2)^2,x)

[Out]

1/7*a^2*x^7+1/4*a*b*x^8+1/9*b^2*x^9

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Maxima [A]  time = 1.3788, size = 32, normalized size = 1.07 \[ \frac{1}{9} \, b^{2} x^{9} + \frac{1}{4} \, a b x^{8} + \frac{1}{7} \, a^{2} x^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*b^2*x^9 + 1/4*a*b*x^8 + 1/7*a^2*x^7

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Fricas [A]  time = 0.195328, size = 1, normalized size = 0.03 \[ \frac{1}{9} x^{9} b^{2} + \frac{1}{4} x^{8} b a + \frac{1}{7} x^{7} a^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*x^9*b^2 + 1/4*x^8*b*a + 1/7*x^7*a^2

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Sympy [A]  time = 0.094223, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{7}}{7} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{9}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a**2*x**7/7 + a*b*x**8/4 + b**2*x**9/9

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GIAC/XCAS [A]  time = 0.216634, size = 32, normalized size = 1.07 \[ \frac{1}{9} \, b^{2} x^{9} + \frac{1}{4} \, a b x^{8} + \frac{1}{7} \, a^{2} x^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*b^2*x^9 + 1/4*a*b*x^8 + 1/7*a^2*x^7