Optimal. Leaf size=75 \[ -\frac{a^3 A}{8 x^8}-\frac{a^2 (a B+3 A b)}{7 x^7}-\frac{b^2 (3 a B+A b)}{5 x^5}-\frac{a b (a B+A b)}{2 x^6}-\frac{b^3 B}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0971536, antiderivative size = 75, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{a^3 A}{8 x^8}-\frac{a^2 (a B+3 A b)}{7 x^7}-\frac{b^2 (3 a B+A b)}{5 x^5}-\frac{a b (a B+A b)}{2 x^6}-\frac{b^3 B}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^3*(A + B*x))/x^9,x]
[Out]
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Rubi in Sympy [A] time = 21.6976, size = 70, normalized size = 0.93 \[ - \frac{A a^{3}}{8 x^{8}} - \frac{B b^{3}}{4 x^{4}} - \frac{a^{2} \left (3 A b + B a\right )}{7 x^{7}} - \frac{a b \left (A b + B a\right )}{2 x^{6}} - \frac{b^{2} \left (A b + 3 B a\right )}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3*(B*x+A)/x**9,x)
[Out]
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Mathematica [A] time = 0.0314434, size = 69, normalized size = 0.92 \[ -\frac{5 a^3 (7 A+8 B x)+20 a^2 b x (6 A+7 B x)+28 a b^2 x^2 (5 A+6 B x)+14 b^3 x^3 (4 A+5 B x)}{280 x^8} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^3*(A + B*x))/x^9,x]
[Out]
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Maple [A] time = 0.009, size = 66, normalized size = 0.9 \[ -{\frac{A{a}^{3}}{8\,{x}^{8}}}-{\frac{{a}^{2} \left ( 3\,Ab+Ba \right ) }{7\,{x}^{7}}}-{\frac{ab \left ( Ab+Ba \right ) }{2\,{x}^{6}}}-{\frac{{b}^{2} \left ( Ab+3\,Ba \right ) }{5\,{x}^{5}}}-{\frac{B{b}^{3}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3*(B*x+A)/x^9,x)
[Out]
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Maxima [A] time = 1.35862, size = 99, normalized size = 1.32 \[ -\frac{70 \, B b^{3} x^{4} + 35 \, A a^{3} + 56 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 140 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 40 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{280 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.197916, size = 99, normalized size = 1.32 \[ -\frac{70 \, B b^{3} x^{4} + 35 \, A a^{3} + 56 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 140 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 40 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{280 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 11.2094, size = 78, normalized size = 1.04 \[ - \frac{35 A a^{3} + 70 B b^{3} x^{4} + x^{3} \left (56 A b^{3} + 168 B a b^{2}\right ) + x^{2} \left (140 A a b^{2} + 140 B a^{2} b\right ) + x \left (120 A a^{2} b + 40 B a^{3}\right )}{280 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3*(B*x+A)/x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.340221, size = 101, normalized size = 1.35 \[ -\frac{70 \, B b^{3} x^{4} + 168 \, B a b^{2} x^{3} + 56 \, A b^{3} x^{3} + 140 \, B a^{2} b x^{2} + 140 \, A a b^{2} x^{2} + 40 \, B a^{3} x + 120 \, A a^{2} b x + 35 \, A a^{3}}{280 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^9,x, algorithm="giac")
[Out]