Optimal. Leaf size=48 \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{3 x^3}-\frac{b (2 a B+A b)}{x}+b^2 B x \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0819563, antiderivative size = 48, 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 \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{3 x^3}-\frac{b (2 a B+A b)}{x}+b^2 B x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^2*(A + B*x^2))/x^6,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{2}}{5 x^{5}} - \frac{a \left (2 A b + B a\right )}{3 x^{3}} + b^{2} \int B\, dx - \frac{b \left (A b + 2 B a\right )}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**2*(B*x**2+A)/x**6,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0344791, size = 48, normalized size = 1. \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{3 x^3}-\frac{b (2 a B+A b)}{x}+b^2 B x \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^2*(A + B*x^2))/x^6,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 45, normalized size = 0.9 \[ -{\frac{A{a}^{2}}{5\,{x}^{5}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{3\,{x}^{3}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{x}}+{b}^{2}Bx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^2*(B*x^2+A)/x^6,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34827, size = 69, normalized size = 1.44 \[ B b^{2} x - \frac{15 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} + 3 \, A a^{2} + 5 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^6,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.22893, size = 72, normalized size = 1.5 \[ \frac{15 \, B b^{2} x^{6} - 15 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} - 3 \, A a^{2} - 5 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^6,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.00719, size = 51, normalized size = 1.06 \[ B b^{2} x - \frac{3 A a^{2} + x^{4} \left (15 A b^{2} + 30 B a b\right ) + x^{2} \left (10 A a b + 5 B a^{2}\right )}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**2*(B*x**2+A)/x**6,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.232235, size = 72, normalized size = 1.5 \[ B b^{2} x - \frac{30 \, B a b x^{4} + 15 \, A b^{2} x^{4} + 5 \, B a^{2} x^{2} + 10 \, A a b x^{2} + 3 \, A a^{2}}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^6,x, algorithm="giac")
[Out]