Optimal. Leaf size=18 \[ -\frac{c^3 (a-b x)^4}{2 x^2} \]
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Rubi [A] time = 0.0169764, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{c^3 (a-b x)^4}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^3)/x^3,x]
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Rubi in Sympy [A] time = 7.24753, size = 15, normalized size = 0.83 \[ - \frac{c^{3} \left (a - b x\right )^{4}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**3/x**3,x)
[Out]
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Mathematica [B] time = 0.0100257, size = 41, normalized size = 2.28 \[ c^3 \left (-\frac{a^4}{2 x^2}+\frac{2 a^3 b}{x}+2 a b^3 x-\frac{b^4 x^2}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^3,x]
[Out]
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Maple [B] time = 0.007, size = 38, normalized size = 2.1 \[{c}^{3} \left ( -{\frac{{b}^{4}{x}^{2}}{2}}+2\,a{b}^{3}x-{\frac{{a}^{4}}{2\,{x}^{2}}}+2\,{\frac{{a}^{3}b}{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^3/x^3,x)
[Out]
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Maxima [A] time = 1.34911, size = 62, normalized size = 3.44 \[ -\frac{1}{2} \, b^{4} c^{3} x^{2} + 2 \, a b^{3} c^{3} x + \frac{4 \, a^{3} b c^{3} x - a^{4} c^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.196202, size = 61, normalized size = 3.39 \[ -\frac{b^{4} c^{3} x^{4} - 4 \, a b^{3} c^{3} x^{3} - 4 \, a^{3} b c^{3} x + a^{4} c^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.695501, size = 46, normalized size = 2.56 \[ 2 a b^{3} c^{3} x - \frac{b^{4} c^{3} x^{2}}{2} + \frac{- a^{4} c^{3} + 4 a^{3} b c^{3} x}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**3/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.327112, size = 62, normalized size = 3.44 \[ -\frac{1}{2} \, b^{4} c^{3} x^{2} + 2 \, a b^{3} c^{3} x + \frac{4 \, a^{3} b c^{3} x - a^{4} c^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^3,x, algorithm="giac")
[Out]