Optimal. Leaf size=26 \[ \frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1) \]
[Out]
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Rubi [A] time = 0.0417843, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1) \]
Antiderivative was successfully verified.
[In] Int[x^3/(2*x + 13*x^2 + 15*x^3),x]
[Out]
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Rubi in Sympy [A] time = 9.94298, size = 20, normalized size = 0.77 \[ \frac{x}{15} - \frac{4 \log{\left (3 x + 2 \right )}}{63} + \frac{\log{\left (5 x + 1 \right )}}{175} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(15*x**3+13*x**2+2*x),x)
[Out]
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Mathematica [A] time = 0.0063219, size = 26, normalized size = 1. \[ \frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1) \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(2*x + 13*x^2 + 15*x^3),x]
[Out]
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Maple [A] time = 0.008, size = 21, normalized size = 0.8 \[{\frac{x}{15}}-{\frac{4\,\ln \left ( 2+3\,x \right ) }{63}}+{\frac{\ln \left ( 1+5\,x \right ) }{175}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(15*x^3+13*x^2+2*x),x)
[Out]
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Maxima [A] time = 0.86591, size = 27, normalized size = 1.04 \[ \frac{1}{15} \, x + \frac{1}{175} \, \log \left (5 \, x + 1\right ) - \frac{4}{63} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(15*x^3 + 13*x^2 + 2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208831, size = 27, normalized size = 1.04 \[ \frac{1}{15} \, x + \frac{1}{175} \, \log \left (5 \, x + 1\right ) - \frac{4}{63} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(15*x^3 + 13*x^2 + 2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.232531, size = 20, normalized size = 0.77 \[ \frac{x}{15} + \frac{\log{\left (x + \frac{1}{5} \right )}}{175} - \frac{4 \log{\left (x + \frac{2}{3} \right )}}{63} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(15*x**3+13*x**2+2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.205726, size = 30, normalized size = 1.15 \[ \frac{1}{15} \, x + \frac{1}{175} \,{\rm ln}\left ({\left | 5 \, x + 1 \right |}\right ) - \frac{4}{63} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(15*x^3 + 13*x^2 + 2*x),x, algorithm="giac")
[Out]