Optimal. Leaf size=30 \[ \frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5} \]
[Out]
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Rubi [A] time = 0.0286132, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 5.01251, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{3}}{3} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.002213, size = 30, normalized size = 1. \[ \frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.002, size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{3}}{3}}+{\frac{ab{x}^{4}}{2}}+{\frac{{b}^{2}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.32527, size = 32, normalized size = 1.07 \[ \frac{1}{5} \, b^{2} x^{5} + \frac{1}{2} \, a b x^{4} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.186504, size = 1, normalized size = 0.03 \[ \frac{1}{5} x^{5} b^{2} + \frac{1}{2} x^{4} b a + \frac{1}{3} x^{3} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.081426, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{3}}{3} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.213879, size = 32, normalized size = 1.07 \[ \frac{1}{5} \, b^{2} x^{5} + \frac{1}{2} \, a b x^{4} + \frac{1}{3} \, a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x^2,x, algorithm="giac")
[Out]