Optimal. Leaf size=18 \[ a^2 c x-\frac{1}{3} b^2 c x^3 \]
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Rubi [A] time = 0.0163604, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ a^2 c x-\frac{1}{3} b^2 c x^3 \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)*(a*c - b*c*x),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} \int c\, dx - \frac{b^{2} c x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c),x)
[Out]
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Mathematica [A] time = 0.00187478, size = 18, normalized size = 1. \[ c \left (a^2 x-\frac{b^2 x^3}{3}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)*(a*c - b*c*x),x]
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Maple [A] time = 0.002, size = 17, normalized size = 0.9 \[{a}^{2}cx-{\frac{{b}^{2}c{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c),x)
[Out]
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Maxima [A] time = 1.34481, size = 22, normalized size = 1.22 \[ -\frac{1}{3} \, b^{2} c x^{3} + a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)*(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.173883, size = 1, normalized size = 0.06 \[ -\frac{1}{3} x^{3} c b^{2} + x c a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)*(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.078144, size = 15, normalized size = 0.83 \[ a^{2} c x - \frac{b^{2} c x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c),x)
[Out]
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GIAC/XCAS [A] time = 0.202479, size = 22, normalized size = 1.22 \[ -\frac{1}{3} \, b^{2} c x^{3} + a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)*(b*x + a),x, algorithm="giac")
[Out]