Optimal. Leaf size=50 \[ -\frac{a^2 A}{8 x^8}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B x \]
[Out]
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Rubi [A] time = 0.090473, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{a^2 A}{8 x^8}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^2*(A + B*x^3))/x^9,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{2}}{8 x^{8}} - \frac{a \left (2 A b + B a\right )}{5 x^{5}} + b^{2} \int B\, dx - \frac{b \left (A b + 2 B a\right )}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(B*x**3+A)/x**9,x)
[Out]
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Mathematica [A] time = 0.04518, size = 50, normalized size = 1. \[ -\frac{a^2 A}{8 x^8}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B x \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^2*(A + B*x^3))/x^9,x]
[Out]
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Maple [A] time = 0.009, size = 45, normalized size = 0.9 \[ -{\frac{A{a}^{2}}{8\,{x}^{8}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{5\,{x}^{5}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{2\,{x}^{2}}}+{b}^{2}Bx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A)/x^9,x)
[Out]
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Maxima [A] time = 1.39796, size = 69, normalized size = 1.38 \[ B b^{2} x - \frac{20 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 8 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + 5 \, A a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217139, size = 72, normalized size = 1.44 \[ \frac{40 \, B b^{2} x^{9} - 20 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} - 8 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 5 \, A a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.33241, size = 51, normalized size = 1.02 \[ B b^{2} x - \frac{5 A a^{2} + x^{6} \left (20 A b^{2} + 40 B a b\right ) + x^{3} \left (16 A a b + 8 B a^{2}\right )}{40 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(B*x**3+A)/x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.214336, size = 72, normalized size = 1.44 \[ B b^{2} x - \frac{40 \, B a b x^{6} + 20 \, A b^{2} x^{6} + 8 \, B a^{2} x^{3} + 16 \, A a b x^{3} + 5 \, A a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^9,x, algorithm="giac")
[Out]