Optimal. Leaf size=31 \[ -\frac{a B+A b}{x}-\frac{a A}{4 x^4}+\frac{1}{2} b B x^2 \]
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Rubi [A] time = 0.0584628, antiderivative size = 31, 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 \[ -\frac{a B+A b}{x}-\frac{a A}{4 x^4}+\frac{1}{2} b B x^2 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)*(A + B*x^3))/x^5,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a}{4 x^{4}} + B b \int x\, dx - \frac{A b + B a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)*(B*x**3+A)/x**5,x)
[Out]
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Mathematica [A] time = 0.0203938, size = 32, normalized size = 1.03 \[ \frac{-a B-A b}{x}-\frac{a A}{4 x^4}+\frac{1}{2} b B x^2 \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)*(A + B*x^3))/x^5,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.9 \[{\frac{bB{x}^{2}}{2}}-{\frac{Aa}{4\,{x}^{4}}}-{\frac{Ab+Ba}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)*(B*x^3+A)/x^5,x)
[Out]
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Maxima [A] time = 1.37096, size = 39, normalized size = 1.26 \[ \frac{1}{2} \, B b x^{2} - \frac{4 \,{\left (B a + A b\right )} x^{3} + A a}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21464, size = 39, normalized size = 1.26 \[ \frac{2 \, B b x^{6} - 4 \,{\left (B a + A b\right )} x^{3} - A a}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.55975, size = 29, normalized size = 0.94 \[ \frac{B b x^{2}}{2} - \frac{A a + x^{3} \left (4 A b + 4 B a\right )}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)*(B*x**3+A)/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.222422, size = 42, normalized size = 1.35 \[ \frac{1}{2} \, B b x^{2} - \frac{4 \, B a x^{3} + 4 \, A b x^{3} + A a}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^5,x, algorithm="giac")
[Out]