Optimal. Leaf size=28 \[ -\frac{a B+A b}{2 x^2}-\frac{a A}{5 x^5}+b B x \]
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Rubi [A] time = 0.0548956, antiderivative size = 28, 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 \[ -\frac{a B+A b}{2 x^2}-\frac{a A}{5 x^5}+b B x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)*(A + B*x^3))/x^6,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a}{5 x^{5}} + b \int B\, dx - \frac{\frac{A b}{2} + \frac{B a}{2}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)*(B*x**3+A)/x**6,x)
[Out]
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Mathematica [A] time = 0.0230193, size = 30, normalized size = 1.07 \[ \frac{-a B-A b}{2 x^2}-\frac{a A}{5 x^5}+b B x \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)*(A + B*x^3))/x^6,x]
[Out]
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Maple [A] time = 0.008, size = 25, normalized size = 0.9 \[ bBx-{\frac{Ab+Ba}{2\,{x}^{2}}}-{\frac{Aa}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)*(B*x^3+A)/x^6,x)
[Out]
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Maxima [A] time = 1.41876, size = 36, normalized size = 1.29 \[ B b x - \frac{5 \,{\left (B a + A b\right )} x^{3} + 2 \, A a}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214746, size = 39, normalized size = 1.39 \[ \frac{10 \, B b x^{6} - 5 \,{\left (B a + A b\right )} x^{3} - 2 \, A a}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.6675, size = 27, normalized size = 0.96 \[ B b x - \frac{2 A a + x^{3} \left (5 A b + 5 B a\right )}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)*(B*x**3+A)/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.223954, size = 39, normalized size = 1.39 \[ B b x - \frac{5 \, B a x^{3} + 5 \, A b x^{3} + 2 \, A a}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^6,x, algorithm="giac")
[Out]