Optimal. Leaf size=26 \[ x (a B+A b)-\frac{a A}{x}+\frac{1}{3} b B x^3 \]
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Rubi [A] time = 0.0484547, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ x (a B+A b)-\frac{a A}{x}+\frac{1}{3} b B x^3 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)*(A + B*x^2))/x^2,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a}{x} + \frac{B b x^{3}}{3} + \frac{\left (A b + B a\right ) \int A\, dx}{A} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)*(B*x**2+A)/x**2,x)
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Mathematica [A] time = 0.0138997, size = 26, normalized size = 1. \[ x (a B+A b)-\frac{a A}{x}+\frac{1}{3} b B x^3 \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)*(A + B*x^2))/x^2,x]
[Out]
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Maple [A] time = 0.006, size = 24, normalized size = 0.9 \[{\frac{bB{x}^{3}}{3}}+Axb+Bxa-{\frac{Aa}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)*(B*x^2+A)/x^2,x)
[Out]
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Maxima [A] time = 1.34501, size = 32, normalized size = 1.23 \[ \frac{1}{3} \, B b x^{3} +{\left (B a + A b\right )} x - \frac{A a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232597, size = 38, normalized size = 1.46 \[ \frac{B b x^{4} + 3 \,{\left (B a + A b\right )} x^{2} - 3 \, A a}{3 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.07721, size = 20, normalized size = 0.77 \[ - \frac{A a}{x} + \frac{B b x^{3}}{3} + x \left (A b + B a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)*(B*x**2+A)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.241363, size = 31, normalized size = 1.19 \[ \frac{1}{3} \, B b x^{3} + B a x + A b x - \frac{A a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^2,x, algorithm="giac")
[Out]