Optimal. Leaf size=40 \[ \frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375} \]
[Out]
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Rubi [A] time = 0.0487612, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ \frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375} \]
Antiderivative was successfully verified.
[In] Int[x^4/(2 + 13*x + 15*x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{3}}{45} - \frac{16 \log{\left (3 x + 2 \right )}}{567} + \frac{\log{\left (5 x + 1 \right )}}{4375} + \int \frac{139}{3375}\, dx - \frac{13 \int x\, dx}{225} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(15*x**2+13*x+2),x)
[Out]
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Mathematica [A] time = 0.0101947, size = 40, normalized size = 1. \[ \frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(2 + 13*x + 15*x^2),x]
[Out]
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Maple [A] time = 0.008, size = 31, normalized size = 0.8 \[{\frac{139\,x}{3375}}-{\frac{13\,{x}^{2}}{450}}+{\frac{{x}^{3}}{45}}-{\frac{16\,\ln \left ( 2+3\,x \right ) }{567}}+{\frac{\ln \left ( 1+5\,x \right ) }{4375}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(15*x^2+13*x+2),x)
[Out]
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Maxima [A] time = 0.830082, size = 41, normalized size = 1.02 \[ \frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log \left (5 \, x + 1\right ) - \frac{16}{567} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(15*x^2 + 13*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210876, size = 41, normalized size = 1.02 \[ \frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log \left (5 \, x + 1\right ) - \frac{16}{567} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(15*x^2 + 13*x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.227323, size = 34, normalized size = 0.85 \[ \frac{x^{3}}{45} - \frac{13 x^{2}}{450} + \frac{139 x}{3375} + \frac{\log{\left (x + \frac{1}{5} \right )}}{4375} - \frac{16 \log{\left (x + \frac{2}{3} \right )}}{567} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(15*x**2+13*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.204662, size = 43, normalized size = 1.08 \[ \frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \,{\rm ln}\left ({\left | 5 \, x + 1 \right |}\right ) - \frac{16}{567} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(15*x^2 + 13*x + 2),x, algorithm="giac")
[Out]