Optimal. Leaf size=35 \[ \frac{(A b-a B) \log \left (a+b x^3\right )}{3 b^2}+\frac{B x^3}{3 b} \]
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Rubi [A] time = 0.10055, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{(A b-a B) \log \left (a+b x^3\right )}{3 b^2}+\frac{B x^3}{3 b} \]
Antiderivative was successfully verified.
[In] Int[(x^2*(A + B*x^3))/(a + b*x^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int ^{x^{3}} B\, dx}{3 b} + \frac{\left (A b - B a\right ) \log{\left (a + b x^{3} \right )}}{3 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(B*x**3+A)/(b*x**3+a),x)
[Out]
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Mathematica [A] time = 0.0221723, size = 31, normalized size = 0.89 \[ \frac{(A b-a B) \log \left (a+b x^3\right )+b B x^3}{3 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[(x^2*(A + B*x^3))/(a + b*x^3),x]
[Out]
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Maple [A] time = 0.003, size = 40, normalized size = 1.1 \[{\frac{B{x}^{3}}{3\,b}}+{\frac{\ln \left ( b{x}^{3}+a \right ) A}{3\,b}}-{\frac{\ln \left ( b{x}^{3}+a \right ) Ba}{3\,{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(B*x^3+A)/(b*x^3+a),x)
[Out]
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Maxima [A] time = 1.37096, size = 42, normalized size = 1.2 \[ \frac{B x^{3}}{3 \, b} - \frac{{\left (B a - A b\right )} \log \left (b x^{3} + a\right )}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*x^2/(b*x^3 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222246, size = 41, normalized size = 1.17 \[ \frac{B b x^{3} -{\left (B a - A b\right )} \log \left (b x^{3} + a\right )}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*x^2/(b*x^3 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.90815, size = 27, normalized size = 0.77 \[ \frac{B x^{3}}{3 b} - \frac{\left (- A b + B a\right ) \log{\left (a + b x^{3} \right )}}{3 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(B*x**3+A)/(b*x**3+a),x)
[Out]
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GIAC/XCAS [A] time = 0.216376, size = 43, normalized size = 1.23 \[ \frac{B x^{3}}{3 \, b} - \frac{{\left (B a - A b\right )}{\rm ln}\left ({\left | b x^{3} + a \right |}\right )}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*x^2/(b*x^3 + a),x, algorithm="giac")
[Out]