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