Optimal. Leaf size=37 \[ -\frac{a^3}{3 x^3}+3 a^2 b \log (x)+a b^2 x^3+\frac{b^3 x^6}{6} \]
[Out]
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Rubi [A] time = 0.0556364, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^3}{3 x^3}+3 a^2 b \log (x)+a b^2 x^3+\frac{b^3 x^6}{6} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3/x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3}}{3 x^{3}} + a^{2} b \log{\left (x^{3} \right )} + a b^{2} x^{3} + \frac{b^{3} \int ^{x^{3}} x\, dx}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3/x**4,x)
[Out]
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Mathematica [A] time = 0.00743577, size = 37, normalized size = 1. \[ -\frac{a^3}{3 x^3}+3 a^2 b \log (x)+a b^2 x^3+\frac{b^3 x^6}{6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3/x^4,x]
[Out]
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Maple [A] time = 0.01, size = 34, normalized size = 0.9 \[ -{\frac{{a}^{3}}{3\,{x}^{3}}}+a{b}^{2}{x}^{3}+{\frac{{b}^{3}{x}^{6}}{6}}+3\,{a}^{2}b\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3/x^4,x)
[Out]
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Maxima [A] time = 1.44406, size = 46, normalized size = 1.24 \[ \frac{1}{6} \, b^{3} x^{6} + a b^{2} x^{3} + a^{2} b \log \left (x^{3}\right ) - \frac{a^{3}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218447, size = 51, normalized size = 1.38 \[ \frac{b^{3} x^{9} + 6 \, a b^{2} x^{6} + 18 \, a^{2} b x^{3} \log \left (x\right ) - 2 \, a^{3}}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.20823, size = 34, normalized size = 0.92 \[ - \frac{a^{3}}{3 x^{3}} + 3 a^{2} b \log{\left (x \right )} + a b^{2} x^{3} + \frac{b^{3} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.218194, size = 59, normalized size = 1.59 \[ \frac{1}{6} \, b^{3} x^{6} + a b^{2} x^{3} + 3 \, a^{2} b{\rm ln}\left ({\left | x \right |}\right ) - \frac{3 \, a^{2} b x^{3} + a^{3}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^4,x, algorithm="giac")
[Out]