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