Optimal. Leaf size=50 \[ A b^2 x+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{3} b x^3 (2 A c+b B)+\frac{1}{7} B c^2 x^7 \]
[Out]
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Rubi [A] time = 0.084784, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ A b^2 x+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{3} b x^3 (2 A c+b B)+\frac{1}{7} B c^2 x^7 \]
Antiderivative was successfully verified.
[In] Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{B c^{2} x^{7}}{7} + b^{2} \int A\, dx + \frac{b x^{3} \left (2 A c + B b\right )}{3} + \frac{c x^{5} \left (A c + 2 B b\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x**2+A)*(c*x**4+b*x**2)**2/x**4,x)
[Out]
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Mathematica [A] time = 0.014404, size = 50, normalized size = 1. \[ A b^2 x+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{3} b x^3 (2 A c+b B)+\frac{1}{7} B c^2 x^7 \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^4,x]
[Out]
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Maple [A] time = 0.001, size = 49, normalized size = 1. \[{\frac{B{c}^{2}{x}^{7}}{7}}+{\frac{ \left ( A{c}^{2}+2\,Bbc \right ){x}^{5}}{5}}+{\frac{ \left ( 2\,Abc+{b}^{2}B \right ){x}^{3}}{3}}+A{b}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x^2+A)*(c*x^4+b*x^2)^2/x^4,x)
[Out]
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Maxima [A] time = 1.36479, size = 65, normalized size = 1.3 \[ \frac{1}{7} \, B c^{2} x^{7} + \frac{1}{5} \,{\left (2 \, B b c + A c^{2}\right )} x^{5} + A b^{2} x + \frac{1}{3} \,{\left (B b^{2} + 2 \, A b c\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*(B*x^2 + A)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216431, size = 65, normalized size = 1.3 \[ \frac{1}{7} \, B c^{2} x^{7} + \frac{1}{5} \,{\left (2 \, B b c + A c^{2}\right )} x^{5} + A b^{2} x + \frac{1}{3} \,{\left (B b^{2} + 2 \, A b c\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*(B*x^2 + A)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.058872, size = 53, normalized size = 1.06 \[ A b^{2} x + \frac{B c^{2} x^{7}}{7} + x^{5} \left (\frac{A c^{2}}{5} + \frac{2 B b c}{5}\right ) + x^{3} \left (\frac{2 A b c}{3} + \frac{B b^{2}}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x**2+A)*(c*x**4+b*x**2)**2/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.206564, size = 68, normalized size = 1.36 \[ \frac{1}{7} \, B c^{2} x^{7} + \frac{2}{5} \, B b c x^{5} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{3} \, B b^{2} x^{3} + \frac{2}{3} \, A b c x^{3} + A b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^2*(B*x^2 + A)/x^4,x, algorithm="giac")
[Out]