Optimal. Leaf size=50 \[ \frac{(A b-a B) \log \left (a+b x^3\right )}{3 a^2}-\frac{\log (x) (A b-a B)}{a^2}-\frac{A}{3 a x^3} \]
[Out]
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Rubi [A] time = 0.138746, antiderivative size = 50, 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 \[ \frac{(A b-a B) \log \left (a+b x^3\right )}{3 a^2}-\frac{\log (x) (A b-a B)}{a^2}-\frac{A}{3 a x^3} \]
Antiderivative was successfully verified.
[In] Int[(A + B*x^3)/(x^4*(a + b*x^3)),x]
[Out]
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Rubi in Sympy [A] time = 14.4592, size = 44, normalized size = 0.88 \[ - \frac{A}{3 a x^{3}} - \frac{\left (A b - B a\right ) \log{\left (x^{3} \right )}}{3 a^{2}} + \frac{\left (A b - B a\right ) \log{\left (a + b x^{3} \right )}}{3 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x**3+A)/x**4/(b*x**3+a),x)
[Out]
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Mathematica [A] time = 0.0380239, size = 49, normalized size = 0.98 \[ \frac{(A b-a B) \log \left (a+b x^3\right )}{3 a^2}+\frac{\log (x) (a B-A b)}{a^2}-\frac{A}{3 a x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(A + B*x^3)/(x^4*(a + b*x^3)),x]
[Out]
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Maple [A] time = 0.009, size = 56, normalized size = 1.1 \[ -{\frac{A}{3\,a{x}^{3}}}-{\frac{A\ln \left ( x \right ) b}{{a}^{2}}}+{\frac{B\ln \left ( x \right ) }{a}}+{\frac{\ln \left ( b{x}^{3}+a \right ) Ab}{3\,{a}^{2}}}-{\frac{\ln \left ( b{x}^{3}+a \right ) B}{3\,a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x^3+A)/x^4/(b*x^3+a),x)
[Out]
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Maxima [A] time = 1.38832, size = 65, normalized size = 1.3 \[ -\frac{{\left (B a - A b\right )} \log \left (b x^{3} + a\right )}{3 \, a^{2}} + \frac{{\left (B a - A b\right )} \log \left (x^{3}\right )}{3 \, a^{2}} - \frac{A}{3 \, a x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)/((b*x^3 + a)*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228558, size = 63, normalized size = 1.26 \[ -\frac{{\left (B a - A b\right )} x^{3} \log \left (b x^{3} + a\right ) - 3 \,{\left (B a - A b\right )} x^{3} \log \left (x\right ) + A a}{3 \, a^{2} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)/((b*x^3 + a)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.81643, size = 41, normalized size = 0.82 \[ - \frac{A}{3 a x^{3}} + \frac{\left (- A b + B a\right ) \log{\left (x \right )}}{a^{2}} - \frac{\left (- A b + B a\right ) \log{\left (\frac{a}{b} + x^{3} \right )}}{3 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x**3+A)/x**4/(b*x**3+a),x)
[Out]
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GIAC/XCAS [A] time = 0.217731, size = 93, normalized size = 1.86 \[ \frac{{\left (B a - A b\right )}{\rm ln}\left ({\left | x \right |}\right )}{a^{2}} - \frac{{\left (B a b - A b^{2}\right )}{\rm ln}\left ({\left | b x^{3} + a \right |}\right )}{3 \, a^{2} b} - \frac{B a x^{3} - A b x^{3} + A a}{3 \, a^{2} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)/((b*x^3 + a)*x^4),x, algorithm="giac")
[Out]