Optimal. Leaf size=31 \[ -\frac{A c+b B}{3 x^3}-\frac{A b}{5 x^5}-\frac{B c}{x} \]
[Out]
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Rubi [A] time = 0.063164, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{A c+b B}{3 x^3}-\frac{A b}{5 x^5}-\frac{B c}{x} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^8,x]
[Out]
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Rubi in Sympy [A] time = 8.18023, size = 27, normalized size = 0.87 \[ - \frac{A b}{5 x^{5}} - \frac{B c}{x} - \frac{\frac{A c}{3} + \frac{B b}{3}}{x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x**2+A)*(c*x**4+b*x**2)/x**8,x)
[Out]
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Mathematica [A] time = 0.019407, size = 33, normalized size = 1.06 \[ \frac{-A c-b B}{3 x^3}-\frac{A b}{5 x^5}-\frac{B c}{x} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x^2)*(b*x^2 + c*x^4))/x^8,x]
[Out]
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Maple [A] time = 0.008, size = 28, normalized size = 0.9 \[ -{\frac{Ac+Bb}{3\,{x}^{3}}}-{\frac{Ab}{5\,{x}^{5}}}-{\frac{Bc}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x^2+A)*(c*x^4+b*x^2)/x^8,x)
[Out]
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Maxima [A] time = 1.37732, size = 39, normalized size = 1.26 \[ -\frac{15 \, B c x^{4} + 5 \,{\left (B b + A c\right )} x^{2} + 3 \, A b}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221486, size = 39, normalized size = 1.26 \[ -\frac{15 \, B c x^{4} + 5 \,{\left (B b + A c\right )} x^{2} + 3 \, A b}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.01271, size = 32, normalized size = 1.03 \[ - \frac{3 A b + 15 B c x^{4} + x^{2} \left (5 A c + 5 B b\right )}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x**2+A)*(c*x**4+b*x**2)/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.205191, size = 42, normalized size = 1.35 \[ -\frac{15 \, B c x^{4} + 5 \, B b x^{2} + 5 \, A c x^{2} + 3 \, A b}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A)/x^8,x, algorithm="giac")
[Out]