Optimal. Leaf size=33 \[ -\frac{a^3}{2 x^2}-\frac{3 a^2 b}{x}+3 a b^2 \log (x)+b^3 x \]
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Rubi [A] time = 0.0296144, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^3}{2 x^2}-\frac{3 a^2 b}{x}+3 a b^2 \log (x)+b^3 x \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^3/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3}}{2 x^{2}} - \frac{3 a^{2} b}{x} + 3 a b^{2} \log{\left (x \right )} + \int b^{3}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3/x**3,x)
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Mathematica [A] time = 0.00710586, size = 33, normalized size = 1. \[ -\frac{a^3}{2 x^2}-\frac{3 a^2 b}{x}+3 a b^2 \log (x)+b^3 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^3/x^3,x]
[Out]
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Maple [A] time = 0.008, size = 32, normalized size = 1. \[ -{\frac{{a}^{3}}{2\,{x}^{2}}}-3\,{\frac{{a}^{2}b}{x}}+{b}^{3}x+3\,a{b}^{2}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3/x^3,x)
[Out]
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Maxima [A] time = 1.32131, size = 41, normalized size = 1.24 \[ b^{3} x + 3 \, a b^{2} \log \left (x\right ) - \frac{6 \, a^{2} b x + a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207257, size = 50, normalized size = 1.52 \[ \frac{2 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} \log \left (x\right ) - 6 \, a^{2} b x - a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.22046, size = 31, normalized size = 0.94 \[ 3 a b^{2} \log{\left (x \right )} + b^{3} x - \frac{a^{3} + 6 a^{2} b x}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.216919, size = 42, normalized size = 1.27 \[ b^{3} x + 3 \, a b^{2}{\rm ln}\left ({\left | x \right |}\right ) - \frac{6 \, a^{2} b x + a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^3,x, algorithm="giac")
[Out]