Optimal. Leaf size=29 \[ \frac{1}{3} x^3 (a B+A b)+a A \log (x)+\frac{1}{6} b B x^6 \]
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Rubi [A] time = 0.0664195, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{1}{3} x^3 (a B+A b)+a A \log (x)+\frac{1}{6} b B x^6 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)*(A + B*x^3))/x,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{A a \log{\left (x^{3} \right )}}{3} + \frac{B b \int ^{x^{3}} x\, dx}{3} + \frac{a \int ^{x^{3}} B\, dx}{3} + \frac{b \int ^{x^{3}} A\, dx}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)*(B*x**3+A)/x,x)
[Out]
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Mathematica [A] time = 0.0161975, size = 29, normalized size = 1. \[ \frac{1}{3} x^3 (a B+A b)+a A \log (x)+\frac{1}{6} b B x^6 \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)*(A + B*x^3))/x,x]
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Maple [A] time = 0.003, size = 28, normalized size = 1. \[{\frac{bB{x}^{6}}{6}}+{\frac{A{x}^{3}b}{3}}+{\frac{B{x}^{3}a}{3}}+aA\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)*(B*x^3+A)/x,x)
[Out]
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Maxima [A] time = 1.36714, size = 38, normalized size = 1.31 \[ \frac{1}{6} \, B b x^{6} + \frac{1}{3} \,{\left (B a + A b\right )} x^{3} + \frac{1}{3} \, A a \log \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224996, size = 34, normalized size = 1.17 \[ \frac{1}{6} \, B b x^{6} + \frac{1}{3} \,{\left (B a + A b\right )} x^{3} + A a \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.04253, size = 27, normalized size = 0.93 \[ A a \log{\left (x \right )} + \frac{B b x^{6}}{6} + x^{3} \left (\frac{A b}{3} + \frac{B a}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)*(B*x**3+A)/x,x)
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GIAC/XCAS [A] time = 0.222875, size = 38, normalized size = 1.31 \[ \frac{1}{6} \, B b x^{6} + \frac{1}{3} \, B a x^{3} + \frac{1}{3} \, A b x^{3} + A a{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x,x, algorithm="giac")
[Out]