Optimal. Leaf size=55 \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0767242, 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 \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^6,x]
[Out]
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Rubi in Sympy [A] time = 20.7874, size = 51, normalized size = 0.93 \[ - \frac{A a^{2}}{5 x^{5}} - \frac{B b^{2}}{2 x^{2}} - \frac{a \left (2 A b + B a\right )}{4 x^{4}} - \frac{b \left (A b + 2 B a\right )}{3 x^{3}} \]
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**6,x)
[Out]
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Mathematica [A] time = 0.0288996, size = 50, normalized size = 0.91 \[ -\frac{3 a^2 (4 A+5 B x)+10 a b x (3 A+4 B x)+10 b^2 x^2 (2 A+3 B x)}{60 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^6,x]
[Out]
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Maple [A] time = 0.007, size = 48, normalized size = 0.9 \[ -{\frac{A{a}^{2}}{5\,{x}^{5}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{4\,{x}^{4}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{3\,{x}^{3}}}-{\frac{{b}^{2}B}{2\,{x}^{2}}} \]
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^6,x)
[Out]
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Maxima [A] time = 0.676312, size = 69, normalized size = 1.25 \[ -\frac{30 \, B b^{2} x^{3} + 12 \, A a^{2} + 20 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 15 \,{\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{5}} \]
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^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.26724, size = 69, normalized size = 1.25 \[ -\frac{30 \, B b^{2} x^{3} + 12 \, A a^{2} + 20 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 15 \,{\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{5}} \]
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^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.8606, size = 54, normalized size = 0.98 \[ - \frac{12 A a^{2} + 30 B b^{2} x^{3} + x^{2} \left (20 A b^{2} + 40 B a b\right ) + x \left (30 A a b + 15 B a^{2}\right )}{60 x^{5}} \]
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**6,x)
[Out]
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GIAC/XCAS [A] time = 0.268944, size = 69, normalized size = 1.25 \[ -\frac{30 \, B b^{2} x^{3} + 40 \, B a b x^{2} + 20 \, A b^{2} x^{2} + 15 \, B a^{2} x + 30 \, A a b x + 12 \, A a^{2}}{60 \, x^{5}} \]
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^6,x, algorithm="giac")
[Out]