Optimal. Leaf size=26 \[ -\frac{a B+A b}{x}-\frac{a A}{3 x^3}+b B x \]
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Rubi [A] time = 0.0497919, 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 \[ -\frac{a B+A b}{x}-\frac{a A}{3 x^3}+b B x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)*(A + B*x^2))/x^4,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a}{3 x^{3}} + b \int B\, dx - \frac{A b + B a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)*(B*x**2+A)/x**4,x)
[Out]
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Mathematica [A] time = 0.0204076, size = 27, normalized size = 1.04 \[ \frac{-a B-A b}{x}-\frac{a A}{3 x^3}+b B x \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)*(A + B*x^2))/x^4,x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 1. \[ bBx-{\frac{Aa}{3\,{x}^{3}}}-{\frac{Ab+Ba}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)*(B*x^2+A)/x^4,x)
[Out]
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Maxima [A] time = 1.34497, size = 35, normalized size = 1.35 \[ B b x - \frac{3 \,{\left (B a + A b\right )} x^{2} + A a}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225187, size = 39, normalized size = 1.5 \[ \frac{3 \, B b x^{4} - 3 \,{\left (B a + A b\right )} x^{2} - A a}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.44718, size = 26, normalized size = 1. \[ B b x - \frac{A a + x^{2} \left (3 A b + 3 B a\right )}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)*(B*x**2+A)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.254484, size = 38, normalized size = 1.46 \[ B b x - \frac{3 \, B a x^{2} + 3 \, A b x^{2} + A a}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^4,x, algorithm="giac")
[Out]