Optimal. Leaf size=50 \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac{1}{4} b^2 B x^4 \]
[Out]
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Rubi [A] time = 0.0937064, 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 \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac{1}{4} b^2 B x^4 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^2*(A + B*x^3))/x^6,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{2}}{5 x^{5}} + \frac{B b^{2} x^{4}}{4} - \frac{a \left (2 A b + B a\right )}{2 x^{2}} + \frac{b \left (A b + 2 B a\right ) \int A\, dx}{A} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(B*x**3+A)/x**6,x)
[Out]
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Mathematica [A] time = 0.0366249, size = 50, normalized size = 1. \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac{1}{4} b^2 B x^4 \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^2*(A + B*x^3))/x^6,x]
[Out]
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Maple [A] time = 0.007, size = 46, normalized size = 0.9 \[{\frac{{b}^{2}B{x}^{4}}{4}}+Ax{b}^{2}+2\,Bxab-{\frac{a \left ( 2\,Ab+Ba \right ) }{2\,{x}^{2}}}-{\frac{A{a}^{2}}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A)/x^6,x)
[Out]
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Maxima [A] time = 1.41779, size = 69, normalized size = 1.38 \[ \frac{1}{4} \, B b^{2} x^{4} +{\left (2 \, B a b + A b^{2}\right )} x - \frac{5 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + 2 \, A a^{2}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221617, size = 72, normalized size = 1.44 \[ \frac{5 \, B b^{2} x^{9} + 20 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} - 10 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 4 \, A a^{2}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.90952, size = 51, normalized size = 1.02 \[ \frac{B b^{2} x^{4}}{4} + x \left (A b^{2} + 2 B a b\right ) - \frac{2 A a^{2} + x^{3} \left (10 A a b + 5 B a^{2}\right )}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(B*x**3+A)/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.212217, size = 69, normalized size = 1.38 \[ \frac{1}{4} \, B b^{2} x^{4} + 2 \, B a b x + A b^{2} x - \frac{5 \, B a^{2} x^{3} + 10 \, A a b x^{3} + 2 \, A a^{2}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^6,x, algorithm="giac")
[Out]