Optimal. Leaf size=33 \[ -\frac{A c+b B}{5 x^5}-\frac{A b}{6 x^6}-\frac{B c}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0413783, 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 \[ -\frac{A c+b B}{5 x^5}-\frac{A b}{6 x^6}-\frac{B c}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2))/x^8,x]
[Out]
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Rubi in Sympy [A] time = 6.97477, size = 31, normalized size = 0.94 \[ - \frac{A b}{6 x^{6}} - \frac{B c}{4 x^{4}} - \frac{\frac{A c}{5} + \frac{B b}{5}}{x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)/x**8,x)
[Out]
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Mathematica [A] time = 0.0154398, size = 31, normalized size = 0.94 \[ -\frac{2 A (5 b+6 c x)+3 B x (4 b+5 c x)}{60 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2))/x^8,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.9 \[ -{\frac{Ab}{6\,{x}^{6}}}-{\frac{Bc}{4\,{x}^{4}}}-{\frac{Ac+Bb}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)/x^8,x)
[Out]
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Maxima [A] time = 0.690789, size = 36, normalized size = 1.09 \[ -\frac{15 \, B c x^{2} + 10 \, A b + 12 \,{\left (B b + A c\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265339, size = 36, normalized size = 1.09 \[ -\frac{15 \, B c x^{2} + 10 \, A b + 12 \,{\left (B b + A c\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.61464, size = 31, normalized size = 0.94 \[ - \frac{10 A b + 15 B c x^{2} + x \left (12 A c + 12 B b\right )}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.26745, size = 36, normalized size = 1.09 \[ -\frac{15 \, B c x^{2} + 12 \, B b x + 12 \, A c x + 10 \, A b}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/x^8,x, algorithm="giac")
[Out]