Optimal. Leaf size=48 \[ \frac{\left (a+b x^2\right )^3 (A b-4 a B)}{24 a^2 x^6}-\frac{A \left (a+b x^2\right )^3}{8 a x^8} \]
[Out]
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Rubi [A] time = 0.107831, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ \frac{\left (a+b x^2\right )^3 (A b-4 a B)}{24 a^2 x^6}-\frac{A \left (a+b x^2\right )^3}{8 a x^8} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^2*(A + B*x^2))/x^9,x]
[Out]
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Rubi in Sympy [A] time = 15.6937, size = 51, normalized size = 1.06 \[ - \frac{A a^{2}}{8 x^{8}} - \frac{B b^{2}}{2 x^{2}} - \frac{a \left (2 A b + B a\right )}{6 x^{6}} - \frac{b \left (A b + 2 B a\right )}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**2*(B*x**2+A)/x**9,x)
[Out]
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Mathematica [A] time = 0.0285649, size = 55, normalized size = 1.15 \[ -\frac{a^2 \left (3 A+4 B x^2\right )+4 a b x^2 \left (2 A+3 B x^2\right )+6 b^2 x^4 \left (A+2 B x^2\right )}{24 x^8} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^2*(A + B*x^2))/x^9,x]
[Out]
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Maple [A] time = 0.008, size = 48, normalized size = 1. \[ -{\frac{a \left ( 2\,Ab+Ba \right ) }{6\,{x}^{6}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{4\,{x}^{4}}}-{\frac{A{a}^{2}}{8\,{x}^{8}}}-{\frac{B{b}^{2}}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^2*(B*x^2+A)/x^9,x)
[Out]
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Maxima [A] time = 1.34502, size = 72, normalized size = 1.5 \[ -\frac{12 \, B b^{2} x^{6} + 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} + 3 \, A a^{2} + 4 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234853, size = 72, normalized size = 1.5 \[ -\frac{12 \, B b^{2} x^{6} + 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} + 3 \, A a^{2} + 4 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.60162, size = 56, normalized size = 1.17 \[ - \frac{3 A a^{2} + 12 B b^{2} x^{6} + x^{4} \left (6 A b^{2} + 12 B a b\right ) + x^{2} \left (8 A a b + 4 B a^{2}\right )}{24 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**2*(B*x**2+A)/x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.221465, size = 74, normalized size = 1.54 \[ -\frac{12 \, B b^{2} x^{6} + 12 \, B a b x^{4} + 6 \, A b^{2} x^{4} + 4 \, B a^{2} x^{2} + 8 \, A a b x^{2} + 3 \, A a^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^9,x, algorithm="giac")
[Out]