Optimal. Leaf size=47 \[ -\frac{a B+A b}{6 x^6}-\frac{a A}{7 x^7}-\frac{A c+b B}{5 x^5}-\frac{B c}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0684421, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ -\frac{a B+A b}{6 x^6}-\frac{a A}{7 x^7}-\frac{A c+b B}{5 x^5}-\frac{B c}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + b*x + c*x^2))/x^8,x]
[Out]
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Rubi in Sympy [A] time = 9.82856, size = 44, normalized size = 0.94 \[ - \frac{A a}{7 x^{7}} - \frac{B c}{4 x^{4}} - \frac{\frac{A c}{5} + \frac{B b}{5}}{x^{5}} - \frac{\frac{A b}{6} + \frac{B a}{6}}{x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x+a)/x**8,x)
[Out]
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Mathematica [A] time = 0.0303904, size = 46, normalized size = 0.98 \[ -\frac{10 a (6 A+7 B x)+7 x (2 A (5 b+6 c x)+3 B x (4 b+5 c x))}{420 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + b*x + c*x^2))/x^8,x]
[Out]
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Maple [A] time = 0.008, size = 40, normalized size = 0.9 \[ -{\frac{Ab+Ba}{6\,{x}^{6}}}-{\frac{Bc}{4\,{x}^{4}}}-{\frac{Ac+Bb}{5\,{x}^{5}}}-{\frac{aA}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x+a)/x^8,x)
[Out]
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Maxima [A] time = 0.69232, size = 53, normalized size = 1.13 \[ -\frac{105 \, B c x^{3} + 84 \,{\left (B b + A c\right )} x^{2} + 60 \, A a + 70 \,{\left (B a + A b\right )} x}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269311, size = 53, normalized size = 1.13 \[ -\frac{105 \, B c x^{3} + 84 \,{\left (B b + A c\right )} x^{2} + 60 \, A a + 70 \,{\left (B a + A b\right )} x}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 14.7637, size = 44, normalized size = 0.94 \[ - \frac{60 A a + 105 B c x^{3} + x^{2} \left (84 A c + 84 B b\right ) + x \left (70 A b + 70 B a\right )}{420 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x+a)/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.27097, size = 55, normalized size = 1.17 \[ -\frac{105 \, B c x^{3} + 84 \, B b x^{2} + 84 \, A c x^{2} + 70 \, B a x + 70 \, A b x + 60 \, A a}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^8,x, algorithm="giac")
[Out]