Optimal. Leaf size=48 \[ -\frac{1}{6 x^3}+\frac{13}{8 x^2}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1) \]
[Out]
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Rubi [A] time = 0.0897364, antiderivative size = 48, 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 \[ -\frac{1}{6 x^3}+\frac{13}{8 x^2}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
[In] Int[1/(x^4*(2 + 13*x + 15*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 12.5313, size = 44, normalized size = 0.92 \[ - \frac{1417 \log{\left (x \right )}}{16} - \frac{81 \log{\left (3 x + 2 \right )}}{112} + \frac{625 \log{\left (5 x + 1 \right )}}{7} - \frac{139}{8 x} + \frac{13}{8 x^{2}} - \frac{1}{6 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(15*x**2+13*x+2),x)
[Out]
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Mathematica [A] time = 0.00903984, size = 48, normalized size = 1. \[ -\frac{1}{6 x^3}+\frac{13}{8 x^2}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^4*(2 + 13*x + 15*x^2)),x]
[Out]
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Maple [A] time = 0.013, size = 37, normalized size = 0.8 \[ -{\frac{1}{6\,{x}^{3}}}+{\frac{13}{8\,{x}^{2}}}-{\frac{139}{8\,x}}-{\frac{1417\,\ln \left ( x \right ) }{16}}-{\frac{81\,\ln \left ( 2+3\,x \right ) }{112}}+{\frac{625\,\ln \left ( 1+5\,x \right ) }{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(15*x^2+13*x+2),x)
[Out]
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Maxima [A] time = 0.839546, size = 49, normalized size = 1.02 \[ -\frac{417 \, x^{2} - 39 \, x + 4}{24 \, x^{3}} + \frac{625}{7} \, \log \left (5 \, x + 1\right ) - \frac{81}{112} \, \log \left (3 \, x + 2\right ) - \frac{1417}{16} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((15*x^2 + 13*x + 2)*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229792, size = 59, normalized size = 1.23 \[ \frac{30000 \, x^{3} \log \left (5 \, x + 1\right ) - 243 \, x^{3} \log \left (3 \, x + 2\right ) - 29757 \, x^{3} \log \left (x\right ) - 5838 \, x^{2} + 546 \, x - 56}{336 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((15*x^2 + 13*x + 2)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.423934, size = 41, normalized size = 0.85 \[ - \frac{1417 \log{\left (x \right )}}{16} + \frac{625 \log{\left (x + \frac{1}{5} \right )}}{7} - \frac{81 \log{\left (x + \frac{2}{3} \right )}}{112} - \frac{417 x^{2} - 39 x + 4}{24 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(15*x**2+13*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.206901, size = 53, normalized size = 1.1 \[ -\frac{417 \, x^{2} - 39 \, x + 4}{24 \, x^{3}} + \frac{625}{7} \,{\rm ln}\left ({\left | 5 \, x + 1 \right |}\right ) - \frac{81}{112} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{1417}{16} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((15*x^2 + 13*x + 2)*x^4),x, algorithm="giac")
[Out]