Optimal. Leaf size=41 \[ -\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1) \]
[Out]
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Rubi [A] time = 0.075715, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*(2 + 13*x + 15*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 12.0558, size = 37, normalized size = 0.9 \[ \frac{139 \log{\left (x \right )}}{8} + \frac{27 \log{\left (3 x + 2 \right )}}{56} - \frac{125 \log{\left (5 x + 1 \right )}}{7} + \frac{13}{4 x} - \frac{1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(15*x**2+13*x+2),x)
[Out]
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Mathematica [A] time = 0.00900112, size = 41, normalized size = 1. \[ -\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*(2 + 13*x + 15*x^2)),x]
[Out]
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Maple [A] time = 0.012, size = 32, normalized size = 0.8 \[ -{\frac{1}{4\,{x}^{2}}}+{\frac{13}{4\,x}}+{\frac{139\,\ln \left ( x \right ) }{8}}+{\frac{27\,\ln \left ( 2+3\,x \right ) }{56}}-{\frac{125\,\ln \left ( 1+5\,x \right ) }{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(15*x^2+13*x+2),x)
[Out]
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Maxima [A] time = 0.849975, size = 42, normalized size = 1.02 \[ \frac{13 \, x - 1}{4 \, x^{2}} - \frac{125}{7} \, \log \left (5 \, x + 1\right ) + \frac{27}{56} \, \log \left (3 \, x + 2\right ) + \frac{139}{8} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((15*x^2 + 13*x + 2)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233496, size = 53, normalized size = 1.29 \[ -\frac{1000 \, x^{2} \log \left (5 \, x + 1\right ) - 27 \, x^{2} \log \left (3 \, x + 2\right ) - 973 \, x^{2} \log \left (x\right ) - 182 \, x + 14}{56 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((15*x^2 + 13*x + 2)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.383366, size = 36, normalized size = 0.88 \[ \frac{139 \log{\left (x \right )}}{8} - \frac{125 \log{\left (x + \frac{1}{5} \right )}}{7} + \frac{27 \log{\left (x + \frac{2}{3} \right )}}{56} + \frac{13 x - 1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(15*x**2+13*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.206145, size = 46, normalized size = 1.12 \[ \frac{13 \, x - 1}{4 \, x^{2}} - \frac{125}{7} \,{\rm ln}\left ({\left | 5 \, x + 1 \right |}\right ) + \frac{27}{56} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{139}{8} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((15*x^2 + 13*x + 2)*x^3),x, algorithm="giac")
[Out]