Optimal. Leaf size=55 \[ -\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{6 x^6}-\frac{b (2 a B+A b)}{5 x^5}-\frac{b^2 B}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0707418, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ -\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{6 x^6}-\frac{b (2 a B+A b)}{5 x^5}-\frac{b^2 B}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^8,x]
[Out]
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Rubi in Sympy [A] time = 20.8644, size = 51, normalized size = 0.93 \[ - \frac{A a^{2}}{7 x^{7}} - \frac{B b^{2}}{4 x^{4}} - \frac{a \left (2 A b + B a\right )}{6 x^{6}} - \frac{b \left (A b + 2 B a\right )}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**8,x)
[Out]
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Mathematica [A] time = 0.027995, size = 50, normalized size = 0.91 \[ -\frac{10 a^2 (6 A+7 B x)+28 a b x (5 A+6 B x)+21 b^2 x^2 (4 A+5 B x)}{420 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^8,x]
[Out]
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Maple [A] time = 0.008, size = 48, normalized size = 0.9 \[ -{\frac{A{a}^{2}}{7\,{x}^{7}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{6\,{x}^{6}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{5\,{x}^{5}}}-{\frac{{b}^{2}B}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^8,x)
[Out]
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Maxima [A] time = 0.677663, size = 69, normalized size = 1.25 \[ -\frac{105 \, B b^{2} x^{3} + 60 \, A a^{2} + 84 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 70 \,{\left (B a^{2} + 2 \, A a b\right )} x}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.3025, size = 69, normalized size = 1.25 \[ -\frac{105 \, B b^{2} x^{3} + 60 \, A a^{2} + 84 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 70 \,{\left (B a^{2} + 2 \, A a b\right )} x}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.31768, size = 54, normalized size = 0.98 \[ - \frac{60 A a^{2} + 105 B b^{2} x^{3} + x^{2} \left (84 A b^{2} + 168 B a b\right ) + x \left (140 A a b + 70 B a^{2}\right )}{420 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.266918, size = 69, normalized size = 1.25 \[ -\frac{105 \, B b^{2} x^{3} + 168 \, B a b x^{2} + 84 \, A b^{2} x^{2} + 70 \, B a^{2} x + 140 \, A a b x + 60 \, A a^{2}}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^8,x, algorithm="giac")
[Out]