Optimal. Leaf size=75 \[ \frac{1}{5} A b^3 x^5+\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{11} c^2 x^{11} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{13} B c^3 x^{13} \]
[Out]
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Rubi [A] time = 0.171348, antiderivative size = 75, 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 \[ \frac{1}{5} A b^3 x^5+\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{11} c^2 x^{11} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{13} B c^3 x^{13} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^2,x]
[Out]
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Rubi in Sympy [A] time = 18.197, size = 68, normalized size = 0.91 \[ \frac{A b^{3} x^{5}}{5} + \frac{B c^{3} x^{13}}{13} + \frac{b^{2} x^{7} \left (3 A c + B b\right )}{7} + \frac{b c x^{9} \left (A c + B b\right )}{3} + \frac{c^{2} x^{11} \left (A c + 3 B b\right )}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x**2+A)*(c*x**4+b*x**2)**3/x**2,x)
[Out]
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Mathematica [A] time = 0.0260002, size = 75, normalized size = 1. \[ \frac{1}{5} A b^3 x^5+\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{11} c^2 x^{11} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{13} B c^3 x^{13} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^2,x]
[Out]
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Maple [A] time = 0.002, size = 76, normalized size = 1. \[{\frac{B{c}^{3}{x}^{13}}{13}}+{\frac{ \left ( A{c}^{3}+3\,Bb{c}^{2} \right ){x}^{11}}{11}}+{\frac{ \left ( 3\,Ab{c}^{2}+3\,B{b}^{2}c \right ){x}^{9}}{9}}+{\frac{ \left ( 3\,A{b}^{2}c+B{b}^{3} \right ){x}^{7}}{7}}+{\frac{A{b}^{3}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x^2+A)*(c*x^4+b*x^2)^3/x^2,x)
[Out]
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Maxima [A] time = 1.37173, size = 99, normalized size = 1.32 \[ \frac{1}{13} \, B c^{3} x^{13} + \frac{1}{11} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{11} + \frac{1}{3} \,{\left (B b^{2} c + A b c^{2}\right )} x^{9} + \frac{1}{5} \, A b^{3} x^{5} + \frac{1}{7} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*(B*x^2 + A)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202526, size = 99, normalized size = 1.32 \[ \frac{1}{13} \, B c^{3} x^{13} + \frac{1}{11} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{11} + \frac{1}{3} \,{\left (B b^{2} c + A b c^{2}\right )} x^{9} + \frac{1}{5} \, A b^{3} x^{5} + \frac{1}{7} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*(B*x^2 + A)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.07116, size = 80, normalized size = 1.07 \[ \frac{A b^{3} x^{5}}{5} + \frac{B c^{3} x^{13}}{13} + x^{11} \left (\frac{A c^{3}}{11} + \frac{3 B b c^{2}}{11}\right ) + x^{9} \left (\frac{A b c^{2}}{3} + \frac{B b^{2} c}{3}\right ) + x^{7} \left (\frac{3 A b^{2} c}{7} + \frac{B b^{3}}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x**2+A)*(c*x**4+b*x**2)**3/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.207459, size = 104, normalized size = 1.39 \[ \frac{1}{13} \, B c^{3} x^{13} + \frac{3}{11} \, B b c^{2} x^{11} + \frac{1}{11} \, A c^{3} x^{11} + \frac{1}{3} \, B b^{2} c x^{9} + \frac{1}{3} \, A b c^{2} x^{9} + \frac{1}{7} \, B b^{3} x^{7} + \frac{3}{7} \, A b^{2} c x^{7} + \frac{1}{5} \, A b^{3} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*(B*x^2 + A)/x^2,x, algorithm="giac")
[Out]