Optimal. Leaf size=53 \[ -\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{x} \]
[Out]
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Rubi [A] time = 0.0817739, antiderivative size = 53, 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 \[ -\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{x} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^2*(A + B*x^2))/x^8,x]
[Out]
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Rubi in Sympy [A] time = 12.9016, size = 48, normalized size = 0.91 \[ - \frac{A a^{2}}{7 x^{7}} - \frac{B b^{2}}{x} - \frac{a \left (2 A b + B a\right )}{5 x^{5}} - \frac{b \left (A b + 2 B a\right )}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**2*(B*x**2+A)/x**8,x)
[Out]
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Mathematica [A] time = 0.0308534, size = 56, normalized size = 1.06 \[ -\frac{3 a^2 \left (5 A+7 B x^2\right )+14 a b x^2 \left (3 A+5 B x^2\right )+35 b^2 x^4 \left (A+3 B x^2\right )}{105 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^2*(A + B*x^2))/x^8,x]
[Out]
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Maple [A] time = 0.007, size = 48, normalized size = 0.9 \[ -{\frac{A{a}^{2}}{7\,{x}^{7}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{5\,{x}^{5}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{3\,{x}^{3}}}-{\frac{B{b}^{2}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^2*(B*x^2+A)/x^8,x)
[Out]
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Maxima [A] time = 1.34511, size = 72, normalized size = 1.36 \[ -\frac{105 \, B b^{2} x^{6} + 35 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} + 15 \, A a^{2} + 21 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220799, size = 72, normalized size = 1.36 \[ -\frac{105 \, B b^{2} x^{6} + 35 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} + 15 \, A a^{2} + 21 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.8222, size = 56, normalized size = 1.06 \[ - \frac{15 A a^{2} + 105 B b^{2} x^{6} + x^{4} \left (35 A b^{2} + 70 B a b\right ) + x^{2} \left (42 A a b + 21 B a^{2}\right )}{105 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**2*(B*x**2+A)/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.227301, size = 74, normalized size = 1.4 \[ -\frac{105 \, B b^{2} x^{6} + 70 \, B a b x^{4} + 35 \, A b^{2} x^{4} + 21 \, B a^{2} x^{2} + 42 \, A a b x^{2} + 15 \, A a^{2}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^8,x, algorithm="giac")
[Out]