Optimal. Leaf size=21 \[ \frac{1}{7} \log (3 x+1)-\frac{1}{7} \log (2-x) \]
[Out]
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Rubi [A] time = 0.0144738, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{1}{7} \log (3 x+1)-\frac{1}{7} \log (2-x) \]
Antiderivative was successfully verified.
[In] Int[(2 + 5*x - 3*x^2)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.65507, size = 14, normalized size = 0.67 \[ - \frac{\log{\left (- x + 2 \right )}}{7} + \frac{\log{\left (3 x + 1 \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-3*x**2+5*x+2),x)
[Out]
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Mathematica [A] time = 0.0052762, size = 21, normalized size = 1. \[ \frac{1}{7} \log (3 x+1)-\frac{1}{7} \log (2-x) \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 5*x - 3*x^2)^(-1),x]
[Out]
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Maple [A] time = 0.008, size = 16, normalized size = 0.8 \[{\frac{\ln \left ( 3\,x+1 \right ) }{7}}-{\frac{\ln \left ( x-2 \right ) }{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-3*x^2+5*x+2),x)
[Out]
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Maxima [A] time = 0.728245, size = 20, normalized size = 0.95 \[ \frac{1}{7} \, \log \left (3 \, x + 1\right ) - \frac{1}{7} \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(3*x^2 - 5*x - 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213459, size = 20, normalized size = 0.95 \[ \frac{1}{7} \, \log \left (3 \, x + 1\right ) - \frac{1}{7} \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(3*x^2 - 5*x - 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.211821, size = 14, normalized size = 0.67 \[ - \frac{\log{\left (x - 2 \right )}}{7} + \frac{\log{\left (x + \frac{1}{3} \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-3*x**2+5*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.210156, size = 23, normalized size = 1.1 \[ \frac{1}{7} \,{\rm ln}\left ({\left | 3 \, x + 1 \right |}\right ) - \frac{1}{7} \,{\rm ln}\left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(3*x^2 - 5*x - 2),x, algorithm="giac")
[Out]