3.218 \(\int x^4 \left (a+b x^3\right )^2 \, dx\)

Optimal. Leaf size=30 \[ \frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11} \]

[Out]

(a^2*x^5)/5 + (a*b*x^8)/4 + (b^2*x^11)/11

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Rubi [A]  time = 0.0336449, 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 \[ \frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11} \]

Antiderivative was successfully verified.

[In]  Int[x^4*(a + b*x^3)^2,x]

[Out]

(a^2*x^5)/5 + (a*b*x^8)/4 + (b^2*x^11)/11

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Rubi in Sympy [A]  time = 5.36491, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{5}}{5} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{11}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**4*(b*x**3+a)**2,x)

[Out]

a**2*x**5/5 + a*b*x**8/4 + b**2*x**11/11

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Mathematica [A]  time = 0.00191926, size = 30, normalized size = 1. \[ \frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11} \]

Antiderivative was successfully verified.

[In]  Integrate[x^4*(a + b*x^3)^2,x]

[Out]

(a^2*x^5)/5 + (a*b*x^8)/4 + (b^2*x^11)/11

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Maple [A]  time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{x}^{5}{a}^{2}}{5}}+{\frac{ab{x}^{8}}{4}}+{\frac{{b}^{2}{x}^{11}}{11}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4*(b*x^3+a)^2,x)

[Out]

1/5*x^5*a^2+1/4*a*b*x^8+1/11*b^2*x^11

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Maxima [A]  time = 1.45128, size = 32, normalized size = 1.07 \[ \frac{1}{11} \, b^{2} x^{11} + \frac{1}{4} \, a b x^{8} + \frac{1}{5} \, a^{2} x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2*x^4,x, algorithm="maxima")

[Out]

1/11*b^2*x^11 + 1/4*a*b*x^8 + 1/5*a^2*x^5

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Fricas [A]  time = 0.189076, size = 1, normalized size = 0.03 \[ \frac{1}{11} x^{11} b^{2} + \frac{1}{4} x^{8} b a + \frac{1}{5} x^{5} a^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2*x^4,x, algorithm="fricas")

[Out]

1/11*x^11*b^2 + 1/4*x^8*b*a + 1/5*x^5*a^2

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Sympy [A]  time = 0.087088, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{5}}{5} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{11}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4*(b*x**3+a)**2,x)

[Out]

a**2*x**5/5 + a*b*x**8/4 + b**2*x**11/11

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GIAC/XCAS [A]  time = 0.212664, size = 32, normalized size = 1.07 \[ \frac{1}{11} \, b^{2} x^{11} + \frac{1}{4} \, a b x^{8} + \frac{1}{5} \, a^{2} x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2*x^4,x, algorithm="giac")

[Out]

1/11*b^2*x^11 + 1/4*a*b*x^8 + 1/5*a^2*x^5