Optimal. Leaf size=33 \[ -\frac{a B+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{b B}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0698478, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{a B+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{b B}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)*(A + B*x^2))/x^7,x]
[Out]
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Rubi in Sympy [A] time = 9.8017, size = 31, normalized size = 0.94 \[ - \frac{A a}{6 x^{6}} - \frac{B b}{2 x^{2}} - \frac{\frac{A b}{4} + \frac{B a}{4}}{x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)*(B*x**2+A)/x**7,x)
[Out]
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Mathematica [A] time = 0.0155557, size = 35, normalized size = 1.06 \[ \frac{-a B-A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{b B}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)*(A + B*x^2))/x^7,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.9 \[ -{\frac{Aa}{6\,{x}^{6}}}-{\frac{Ab+Ba}{4\,{x}^{4}}}-{\frac{Bb}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)*(B*x^2+A)/x^7,x)
[Out]
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Maxima [A] time = 1.33117, size = 39, normalized size = 1.18 \[ -\frac{6 \, B b x^{4} + 3 \,{\left (B a + A b\right )} x^{2} + 2 \, A a}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2279, size = 39, normalized size = 1.18 \[ -\frac{6 \, B b x^{4} + 3 \,{\left (B a + A b\right )} x^{2} + 2 \, A a}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.61765, size = 32, normalized size = 0.97 \[ - \frac{2 A a + 6 B b x^{4} + x^{2} \left (3 A b + 3 B a\right )}{12 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)*(B*x**2+A)/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.282054, size = 42, normalized size = 1.27 \[ -\frac{6 \, B b x^{4} + 3 \, B a x^{2} + 3 \, A b x^{2} + 2 \, A a}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)/x^7,x, algorithm="giac")
[Out]