Optimal. Leaf size=45 \[ -\frac{a^4 c^3}{3 x^3}+\frac{a^3 b c^3}{x^2}+2 a b^3 c^3 \log (x)-b^4 c^3 x \]
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Rubi [A] time = 0.0647815, antiderivative size = 45, 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 \[ -\frac{a^4 c^3}{3 x^3}+\frac{a^3 b c^3}{x^2}+2 a b^3 c^3 \log (x)-b^4 c^3 x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^3)/x^4,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{4} c^{3}}{3 x^{3}} + \frac{a^{3} b c^{3}}{x^{2}} + 2 a b^{3} c^{3} \log{\left (x \right )} - c^{3} \int b^{4}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**3/x**4,x)
[Out]
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Mathematica [A] time = 0.0105812, size = 37, normalized size = 0.82 \[ c^3 \left (-\frac{a^4}{3 x^3}+\frac{a^3 b}{x^2}+2 a b^3 \log (x)-b^4 x\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^4,x]
[Out]
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Maple [A] time = 0.008, size = 44, normalized size = 1. \[ -{\frac{{a}^{4}{c}^{3}}{3\,{x}^{3}}}+{\frac{{a}^{3}b{c}^{3}}{{x}^{2}}}-{b}^{4}{c}^{3}x+2\,a{b}^{3}{c}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^3/x^4,x)
[Out]
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Maxima [A] time = 1.34687, size = 61, normalized size = 1.36 \[ -b^{4} c^{3} x + 2 \, a b^{3} c^{3} \log \left (x\right ) + \frac{3 \, a^{3} b c^{3} x - a^{4} c^{3}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206879, size = 65, normalized size = 1.44 \[ -\frac{3 \, b^{4} c^{3} x^{4} - 6 \, a b^{3} c^{3} x^{3} \log \left (x\right ) - 3 \, a^{3} b c^{3} x + a^{4} c^{3}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.793751, size = 44, normalized size = 0.98 \[ 2 a b^{3} c^{3} \log{\left (x \right )} - b^{4} c^{3} x + \frac{- a^{4} c^{3} + 3 a^{3} b c^{3} x}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**3/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.324626, size = 62, normalized size = 1.38 \[ -b^{4} c^{3} x + 2 \, a b^{3} c^{3}{\rm ln}\left ({\left | x \right |}\right ) + \frac{3 \, a^{3} b c^{3} x - a^{4} c^{3}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^4,x, algorithm="giac")
[Out]