Optimal. Leaf size=18 \[ \frac{\log (x)}{a}-\frac{\log (a+b x)}{a} \]
[Out]
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Rubi [A] time = 0.0219345, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ \frac{\log (x)}{a}-\frac{\log (a+b x)}{a} \]
Antiderivative was successfully verified.
[In] Int[x/(a*x^2 + b*x^3),x]
[Out]
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Rubi in Sympy [A] time = 4.5208, size = 12, normalized size = 0.67 \[ \frac{\log{\left (x \right )}}{a} - \frac{\log{\left (a + b x \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x**3+a*x**2),x)
[Out]
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Mathematica [A] time = 0.0056813, size = 18, normalized size = 1. \[ \frac{\log (x)}{a}-\frac{\log (a+b x)}{a} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a*x^2 + b*x^3),x]
[Out]
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Maple [A] time = 0.008, size = 19, normalized size = 1.1 \[{\frac{\ln \left ( x \right ) }{a}}-{\frac{\ln \left ( bx+a \right ) }{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x^3+a*x^2),x)
[Out]
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Maxima [A] time = 1.38077, size = 24, normalized size = 1.33 \[ -\frac{\log \left (b x + a\right )}{a} + \frac{\log \left (x\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^3 + a*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213362, size = 22, normalized size = 1.22 \[ -\frac{\log \left (b x + a\right ) - \log \left (x\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^3 + a*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.335426, size = 10, normalized size = 0.56 \[ \frac{\log{\left (x \right )} - \log{\left (\frac{a}{b} + x \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x**3+a*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.218869, size = 27, normalized size = 1.5 \[ -\frac{{\rm ln}\left ({\left | b x + a \right |}\right )}{a} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^3 + a*x^2),x, algorithm="giac")
[Out]