Optimal. Leaf size=27 \[ \frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1) \]
[Out]
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Rubi [A] time = 0.0369612, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.312 \[ \frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
[In] Int[(2*x + 13*x^2 + 15*x^3)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 7.27133, size = 24, normalized size = 0.89 \[ \frac{\log{\left (x \right )}}{2} + \frac{3 \log{\left (3 x + 2 \right )}}{14} - \frac{5 \log{\left (5 x + 1 \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(15*x**3+13*x**2+2*x),x)
[Out]
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Mathematica [A] time = 0.00692891, size = 27, normalized size = 1. \[ \frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(2*x + 13*x^2 + 15*x^3)^(-1),x]
[Out]
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Maple [A] time = 0.009, size = 22, normalized size = 0.8 \[{\frac{\ln \left ( x \right ) }{2}}+{\frac{3\,\ln \left ( 2+3\,x \right ) }{14}}-{\frac{5\,\ln \left ( 1+5\,x \right ) }{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(15*x^3+13*x^2+2*x),x)
[Out]
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Maxima [A] time = 0.868293, size = 28, normalized size = 1.04 \[ -\frac{5}{7} \, \log \left (5 \, x + 1\right ) + \frac{3}{14} \, \log \left (3 \, x + 2\right ) + \frac{1}{2} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15*x^3 + 13*x^2 + 2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214018, size = 28, normalized size = 1.04 \[ -\frac{5}{7} \, \log \left (5 \, x + 1\right ) + \frac{3}{14} \, \log \left (3 \, x + 2\right ) + \frac{1}{2} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15*x^3 + 13*x^2 + 2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.28759, size = 24, normalized size = 0.89 \[ \frac{\log{\left (x \right )}}{2} - \frac{5 \log{\left (x + \frac{1}{5} \right )}}{7} + \frac{3 \log{\left (x + \frac{2}{3} \right )}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15*x**3+13*x**2+2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.205187, size = 32, normalized size = 1.19 \[ -\frac{5}{7} \,{\rm ln}\left ({\left | 5 \, x + 1 \right |}\right ) + \frac{3}{14} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{1}{2} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15*x^3 + 13*x^2 + 2*x),x, algorithm="giac")
[Out]