Optimal. Leaf size=28 \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3 \]
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Rubi [A] time = 0.0414372, antiderivative size = 28, 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 \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3 \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)*(A + B*x),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{B b x^{3}}{3} + a \int A\, dx + \left (A b + B a\right ) \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A),x)
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Mathematica [A] time = 0.00747448, size = 28, normalized size = 1. \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} b B x^3 \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)*(A + B*x),x]
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Maple [A] time = 0.002, size = 25, normalized size = 0.9 \[ aAx+{\frac{ \left ( Ab+Ba \right ){x}^{2}}{2}}+{\frac{bB{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A),x)
[Out]
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Maxima [A] time = 1.35983, size = 32, normalized size = 1.14 \[ \frac{1}{3} \, B b x^{3} + A a x + \frac{1}{2} \,{\left (B a + A b\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a),x, algorithm="maxima")
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Fricas [A] time = 0.191306, size = 1, normalized size = 0.04 \[ \frac{1}{3} x^{3} b B + \frac{1}{2} x^{2} a B + \frac{1}{2} x^{2} b A + x a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.071371, size = 26, normalized size = 0.93 \[ A a x + \frac{B b x^{3}}{3} + x^{2} \left (\frac{A b}{2} + \frac{B a}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.211776, size = 35, normalized size = 1.25 \[ \frac{1}{3} \, B b x^{3} + \frac{1}{2} \, B a x^{2} + \frac{1}{2} \, A b x^{2} + A a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a),x, algorithm="giac")
[Out]