Optimal. Leaf size=50 \[ -\frac{a^4 c^3}{5 x^5}+\frac{a^3 b c^3}{2 x^4}-\frac{a b^3 c^3}{x^2}+\frac{b^4 c^3}{x} \]
[Out]
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Rubi [A] time = 0.0658317, antiderivative size = 50, 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 \[ -\frac{a^4 c^3}{5 x^5}+\frac{a^3 b c^3}{2 x^4}-\frac{a b^3 c^3}{x^2}+\frac{b^4 c^3}{x} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^3)/x^6,x]
[Out]
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Rubi in Sympy [A] time = 19.3438, size = 44, normalized size = 0.88 \[ - \frac{a^{4} c^{3}}{5 x^{5}} + \frac{a^{3} b c^{3}}{2 x^{4}} - \frac{a b^{3} c^{3}}{x^{2}} + \frac{b^{4} c^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**3/x**6,x)
[Out]
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Mathematica [A] time = 0.00945838, size = 42, normalized size = 0.84 \[ c^3 \left (-\frac{a^4}{5 x^5}+\frac{a^3 b}{2 x^4}-\frac{a b^3}{x^2}+\frac{b^4}{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^6,x]
[Out]
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Maple [A] time = 0.009, size = 39, normalized size = 0.8 \[{c}^{3} \left ( -{\frac{a{b}^{3}}{{x}^{2}}}-{\frac{{a}^{4}}{5\,{x}^{5}}}+{\frac{{b}^{4}}{x}}+{\frac{{a}^{3}b}{2\,{x}^{4}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^3/x^6,x)
[Out]
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Maxima [A] time = 1.33919, size = 63, normalized size = 1.26 \[ \frac{10 \, b^{4} c^{3} x^{4} - 10 \, a b^{3} c^{3} x^{3} + 5 \, a^{3} b c^{3} x - 2 \, a^{4} c^{3}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200824, size = 63, normalized size = 1.26 \[ \frac{10 \, b^{4} c^{3} x^{4} - 10 \, a b^{3} c^{3} x^{3} + 5 \, a^{3} b c^{3} x - 2 \, a^{4} c^{3}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.967409, size = 49, normalized size = 0.98 \[ \frac{- 2 a^{4} c^{3} + 5 a^{3} b c^{3} x - 10 a b^{3} c^{3} x^{3} + 10 b^{4} c^{3} x^{4}}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**3/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.257344, size = 63, normalized size = 1.26 \[ \frac{10 \, b^{4} c^{3} x^{4} - 10 \, a b^{3} c^{3} x^{3} + 5 \, a^{3} b c^{3} x - 2 \, a^{4} c^{3}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^6,x, algorithm="giac")
[Out]