Optimal. Leaf size=30 \[ \frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7} \]
[Out]
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Rubi [A] time = 0.0305165, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7} \]
Antiderivative was successfully verified.
[In] Int[(a*x + b*x^3)^2,x]
[Out]
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Rubi in Sympy [A] time = 3.1807, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{3}}{3} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a*x)**2,x)
[Out]
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Mathematica [A] time = 0.00240467, size = 30, normalized size = 1. \[ \frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x + b*x^3)^2,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{3}}{3}}+{\frac{2\,ab{x}^{5}}{5}}+{\frac{{b}^{2}{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a*x)^2,x)
[Out]
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Maxima [A] time = 6.90061, size = 32, normalized size = 1.07 \[ \frac{1}{7} \, b^{2} x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.180703, size = 1, normalized size = 0.03 \[ \frac{1}{7} x^{7} b^{2} + \frac{2}{5} x^{5} b a + \frac{1}{3} x^{3} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.047495, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{3}}{3} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.216756, size = 32, normalized size = 1.07 \[ \frac{1}{7} \, b^{2} x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x)^2,x, algorithm="giac")
[Out]