Optimal. Leaf size=30 \[ \frac{1}{5 (1-x)}-\frac{1}{25} \log (1-x)+\frac{1}{25} \log (x+4) \]
[Out]
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Rubi [A] time = 0.0243878, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{5 (1-x)}-\frac{1}{25} \log (1-x)+\frac{1}{25} \log (x+4) \]
Antiderivative was successfully verified.
[In] Int[1/((-1 + x)^2*(4 + x)),x]
[Out]
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Rubi in Sympy [A] time = 1.78079, size = 19, normalized size = 0.63 \[ - \frac{\log{\left (- x + 1 \right )}}{25} + \frac{\log{\left (x + 4 \right )}}{25} + \frac{1}{5 \left (- x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-1+x)**2/(4+x),x)
[Out]
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Mathematica [A] time = 0.0120141, size = 22, normalized size = 0.73 \[ \frac{1}{25} \left (-\frac{5}{x-1}-\log (x-1)+\log (x+4)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/((-1 + x)^2*(4 + x)),x]
[Out]
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Maple [A] time = 0.01, size = 21, normalized size = 0.7 \[{\frac{\ln \left ( 4+x \right ) }{25}}-{\frac{1}{-5+5\,x}}-{\frac{\ln \left ( -1+x \right ) }{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-1+x)^2/(4+x),x)
[Out]
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Maxima [A] time = 1.36408, size = 27, normalized size = 0.9 \[ -\frac{1}{5 \,{\left (x - 1\right )}} + \frac{1}{25} \, \log \left (x + 4\right ) - \frac{1}{25} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 4)*(x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204318, size = 35, normalized size = 1.17 \[ \frac{{\left (x - 1\right )} \log \left (x + 4\right ) -{\left (x - 1\right )} \log \left (x - 1\right ) - 5}{25 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 4)*(x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.118058, size = 19, normalized size = 0.63 \[ - \frac{\log{\left (x - 1 \right )}}{25} + \frac{\log{\left (x + 4 \right )}}{25} - \frac{1}{5 x - 5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-1+x)**2/(4+x),x)
[Out]
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GIAC/XCAS [A] time = 0.20437, size = 28, normalized size = 0.93 \[ -\frac{1}{5 \,{\left (x - 1\right )}} + \frac{1}{25} \,{\rm ln}\left ({\left | -\frac{5}{x - 1} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 4)*(x - 1)^2),x, algorithm="giac")
[Out]