Optimal. Leaf size=55 \[ -\frac{a^4 c^3}{6 x^6}+\frac{2 a^3 b c^3}{5 x^5}-\frac{2 a b^3 c^3}{3 x^3}+\frac{b^4 c^3}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0679135, antiderivative size = 55, 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 \[ -\frac{a^4 c^3}{6 x^6}+\frac{2 a^3 b c^3}{5 x^5}-\frac{2 a b^3 c^3}{3 x^3}+\frac{b^4 c^3}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^3)/x^7,x]
[Out]
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Rubi in Sympy [A] time = 19.6266, size = 53, normalized size = 0.96 \[ - \frac{a^{4} c^{3}}{6 x^{6}} + \frac{2 a^{3} b c^{3}}{5 x^{5}} - \frac{2 a b^{3} c^{3}}{3 x^{3}} + \frac{b^{4} c^{3}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**3/x**7,x)
[Out]
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Mathematica [A] time = 0.00965933, size = 47, normalized size = 0.85 \[ c^3 \left (-\frac{a^4}{6 x^6}+\frac{2 a^3 b}{5 x^5}-\frac{2 a b^3}{3 x^3}+\frac{b^4}{2 x^2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^7,x]
[Out]
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Maple [A] time = 0.007, size = 40, normalized size = 0.7 \[{c}^{3} \left ({\frac{{b}^{4}}{2\,{x}^{2}}}+{\frac{2\,{a}^{3}b}{5\,{x}^{5}}}-{\frac{2\,a{b}^{3}}{3\,{x}^{3}}}-{\frac{{a}^{4}}{6\,{x}^{6}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^3/x^7,x)
[Out]
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Maxima [A] time = 1.34674, size = 63, normalized size = 1.15 \[ \frac{15 \, b^{4} c^{3} x^{4} - 20 \, a b^{3} c^{3} x^{3} + 12 \, a^{3} b c^{3} x - 5 \, a^{4} c^{3}}{30 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199403, size = 63, normalized size = 1.15 \[ \frac{15 \, b^{4} c^{3} x^{4} - 20 \, a b^{3} c^{3} x^{3} + 12 \, a^{3} b c^{3} x - 5 \, a^{4} c^{3}}{30 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.928871, size = 49, normalized size = 0.89 \[ \frac{- 5 a^{4} c^{3} + 12 a^{3} b c^{3} x - 20 a b^{3} c^{3} x^{3} + 15 b^{4} c^{3} x^{4}}{30 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**3/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.2405, size = 63, normalized size = 1.15 \[ \frac{15 \, b^{4} c^{3} x^{4} - 20 \, a b^{3} c^{3} x^{3} + 12 \, a^{3} b c^{3} x - 5 \, a^{4} c^{3}}{30 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^7,x, algorithm="giac")
[Out]