Optimal. Leaf size=31 \[ a A x+\frac{B \left (a+c x^2\right )^2}{4 c}+\frac{1}{3} A c x^3 \]
[Out]
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Rubi [A] time = 0.0224007, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ a A x+\frac{B \left (a+c x^2\right )^2}{4 c}+\frac{1}{3} A c x^3 \]
Antiderivative was successfully verified.
[In] Int[(A + B*x)*(a + c*x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{A c x^{3}}{3} + B a \int x\, dx + \frac{B c x^{4}}{4} + a \int A\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+a),x)
[Out]
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Mathematica [A] time = 0.00276625, size = 32, normalized size = 1.03 \[ a A x+\frac{1}{2} a B x^2+\frac{1}{3} A c x^3+\frac{1}{4} B c x^4 \]
Antiderivative was successfully verified.
[In] Integrate[(A + B*x)*(a + c*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 27, normalized size = 0.9 \[{\frac{Bc{x}^{4}}{4}}+{\frac{Ac{x}^{3}}{3}}+{\frac{aB{x}^{2}}{2}}+aAx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+a),x)
[Out]
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Maxima [A] time = 0.690866, size = 35, normalized size = 1.13 \[ \frac{1}{4} \, B c x^{4} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + A a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271476, size = 1, normalized size = 0.03 \[ \frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} a B + x a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.081972, size = 29, normalized size = 0.94 \[ A a x + \frac{A c x^{3}}{3} + \frac{B a x^{2}}{2} + \frac{B c x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.266647, size = 35, normalized size = 1.13 \[ \frac{1}{4} \, B c x^{4} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + A a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A),x, algorithm="giac")
[Out]