Optimal. Leaf size=27 \[ \frac{99}{x+3}+\frac{181}{x+4}+264 \log (x+3)-263 \log (x+4) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.04577, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{99}{x+3}+\frac{181}{x+4}+264 \log (x+3)-263 \log (x+4) \]
Antiderivative was successfully verified.
[In] Int[(-9 + 3*x - 6*x^2 + x^3)/((3 + x)^2*(4 + x)^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{3} - 6 x^{2} + 3 x - 9}{\left (x + 3\right )^{2} \left (x + 4\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3-6*x**2+3*x-9)/(3+x)**2/(4+x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0250112, size = 27, normalized size = 1. \[ \frac{99}{x+3}+\frac{181}{x+4}+264 \log (x+3)-263 \log (x+4) \]
Antiderivative was successfully verified.
[In] Integrate[(-9 + 3*x - 6*x^2 + x^3)/((3 + x)^2*(4 + x)^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.015, size = 28, normalized size = 1. \[ 99\, \left ( 3+x \right ) ^{-1}+181\, \left ( 4+x \right ) ^{-1}+264\,\ln \left ( 3+x \right ) -263\,\ln \left ( 4+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3-6*x^2+3*x-9)/(3+x)^2/(4+x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33281, size = 39, normalized size = 1.44 \[ \frac{280 \, x + 939}{x^{2} + 7 \, x + 12} - 263 \, \log \left (x + 4\right ) + 264 \, \log \left (x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 6*x^2 + 3*x - 9)/((x + 4)^2*(x + 3)^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.194637, size = 61, normalized size = 2.26 \[ -\frac{263 \,{\left (x^{2} + 7 \, x + 12\right )} \log \left (x + 4\right ) - 264 \,{\left (x^{2} + 7 \, x + 12\right )} \log \left (x + 3\right ) - 280 \, x - 939}{x^{2} + 7 \, x + 12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 6*x^2 + 3*x - 9)/((x + 4)^2*(x + 3)^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.159509, size = 26, normalized size = 0.96 \[ \frac{280 x + 939}{x^{2} + 7 x + 12} + 264 \log{\left (x + 3 \right )} - 263 \log{\left (x + 4 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3-6*x**2+3*x-9)/(3+x)**2/(4+x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.20252, size = 50, normalized size = 1.85 \[ \frac{181}{x + 4} - \frac{99}{\frac{1}{x + 4} - 1} +{\rm ln}\left ({\left | x + 4 \right |}\right ) + 264 \,{\rm ln}\left ({\left | -\frac{1}{x + 4} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 6*x^2 + 3*x - 9)/((x + 4)^2*(x + 3)^2),x, algorithm="giac")
[Out]