Optimal. Leaf size=65 \[ -\frac{A b^3}{x}+b^2 x (3 A c+b B)+\frac{1}{5} c^2 x^5 (A c+3 b B)+b c x^3 (A c+b B)+\frac{1}{7} B c^3 x^7 \]
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Rubi [A] time = 0.125101, antiderivative size = 65, 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 \[ -\frac{A b^3}{x}+b^2 x (3 A c+b B)+\frac{1}{5} c^2 x^5 (A c+3 b B)+b c x^3 (A c+b B)+\frac{1}{7} B c^3 x^7 \]
Antiderivative was successfully verified.
[In] Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^8,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A b^{3}}{x} + \frac{B c^{3} x^{7}}{7} + b c x^{3} \left (A c + B b\right ) + \frac{c^{2} x^{5} \left (A c + 3 B b\right )}{5} + \frac{b^{2} \left (3 A c + B b\right ) \int B\, dx}{B} \]
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**8,x)
[Out]
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Mathematica [A] time = 0.0404254, size = 65, normalized size = 1. \[ -\frac{A b^3}{x}+b^2 x (3 A c+b B)+\frac{1}{5} c^2 x^5 (A c+3 b B)+b c x^3 (A c+b B)+\frac{1}{7} B c^3 x^7 \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^8,x]
[Out]
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Maple [A] time = 0.006, size = 71, normalized size = 1.1 \[{\frac{B{c}^{3}{x}^{7}}{7}}+{\frac{A{x}^{5}{c}^{3}}{5}}+{\frac{3\,B{x}^{5}b{c}^{2}}{5}}+A{x}^{3}b{c}^{2}+B{x}^{3}{b}^{2}c+3\,Ax{b}^{2}c+Bx{b}^{3}-{\frac{A{b}^{3}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x^2+A)*(c*x^4+b*x^2)^3/x^8,x)
[Out]
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Maxima [A] time = 1.37591, size = 93, normalized size = 1.43 \[ \frac{1}{7} \, B c^{3} x^{7} + \frac{1}{5} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{5} +{\left (B b^{2} c + A b c^{2}\right )} x^{3} - \frac{A b^{3}}{x} +{\left (B b^{3} + 3 \, A b^{2} c\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*(B*x^2 + A)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199088, size = 101, normalized size = 1.55 \[ \frac{5 \, B c^{3} x^{8} + 7 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{6} + 35 \,{\left (B b^{2} c + A b c^{2}\right )} x^{4} - 35 \, A b^{3} + 35 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{2}}{35 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*(B*x^2 + A)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.631553, size = 68, normalized size = 1.05 \[ - \frac{A b^{3}}{x} + \frac{B c^{3} x^{7}}{7} + x^{5} \left (\frac{A c^{3}}{5} + \frac{3 B b c^{2}}{5}\right ) + x^{3} \left (A b c^{2} + B b^{2} c\right ) + x \left (3 A b^{2} c + B b^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x**2+A)*(c*x**4+b*x**2)**3/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.206951, size = 95, normalized size = 1.46 \[ \frac{1}{7} \, B c^{3} x^{7} + \frac{3}{5} \, B b c^{2} x^{5} + \frac{1}{5} \, A c^{3} x^{5} + B b^{2} c x^{3} + A b c^{2} x^{3} + B b^{3} x + 3 \, A b^{2} c x - \frac{A b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*(B*x^2 + A)/x^8,x, algorithm="giac")
[Out]