Optimal. Leaf size=50 \[ -\frac{a^2 A}{2 x^2}+\frac{1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{7} b^2 B x^7 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0907577, 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 \[ -\frac{a^2 A}{2 x^2}+\frac{1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{7} b^2 B x^7 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^2*(A + B*x^3))/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{2}}{2 x^{2}} + \frac{B b^{2} x^{7}}{7} + \frac{b x^{4} \left (A b + 2 B a\right )}{4} + \frac{a \left (2 A b + B a\right ) \int B\, dx}{B} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(B*x**3+A)/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0323813, size = 50, normalized size = 1. \[ -\frac{a^2 A}{2 x^2}+\frac{1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{7} b^2 B x^7 \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^2*(A + B*x^3))/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 49, normalized size = 1. \[{\frac{{b}^{2}B{x}^{7}}{7}}+{\frac{A{x}^{4}{b}^{2}}{4}}+{\frac{B{x}^{4}ab}{2}}+2\,Axab+Bx{a}^{2}-{\frac{A{a}^{2}}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A)/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.47794, size = 65, normalized size = 1.3 \[ \frac{1}{7} \, B b^{2} x^{7} + \frac{1}{4} \,{\left (2 \, B a b + A b^{2}\right )} x^{4} +{\left (B a^{2} + 2 \, A a b\right )} x - \frac{A a^{2}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.210151, size = 72, normalized size = 1.44 \[ \frac{4 \, B b^{2} x^{9} + 7 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 28 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 14 \, A a^{2}}{28 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.16922, size = 49, normalized size = 0.98 \[ - \frac{A a^{2}}{2 x^{2}} + \frac{B b^{2} x^{7}}{7} + x^{4} \left (\frac{A b^{2}}{4} + \frac{B a b}{2}\right ) + x \left (2 A a b + B a^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(B*x**3+A)/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.213079, size = 65, normalized size = 1.3 \[ \frac{1}{7} \, B b^{2} x^{7} + \frac{1}{2} \, B a b x^{4} + \frac{1}{4} \, A b^{2} x^{4} + B a^{2} x + 2 \, A a b x - \frac{A a^{2}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^3,x, algorithm="giac")
[Out]