Optimal. Leaf size=17 \[ \frac{a x^3}{3}+\frac{b x^4}{4} \]
[Out]
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Rubi [A] time = 0.0187523, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{a x^3}{3}+\frac{b x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 2.52632, size = 12, normalized size = 0.71 \[ \frac{a x^{3}}{3} + \frac{b x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00130265, size = 17, normalized size = 1. \[ \frac{a x^3}{3}+\frac{b x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x),x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.8 \[{\frac{a{x}^{3}}{3}}+{\frac{b{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x+a),x)
[Out]
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Maxima [A] time = 1.3198, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.189209, size = 1, normalized size = 0.06 \[ \frac{1}{4} x^{4} b + \frac{1}{3} x^{3} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.061064, size = 12, normalized size = 0.71 \[ \frac{a x^{3}}{3} + \frac{b x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.210514, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^2,x, algorithm="giac")
[Out]