Optimal. Leaf size=21 \[ -\frac{3 \log (x)}{2}+4 \log (x+1)-\frac{5}{2} \log (x+2) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0476858, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{3 \log (x)}{2}+4 \log (x+1)-\frac{5}{2} \log (x+2) \]
Antiderivative was successfully verified.
[In] Int[(-3 + x)/(2*x + 3*x^2 + x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 12.6167, size = 20, normalized size = 0.95 \[ - \frac{3 \log{\left (x \right )}}{2} + 4 \log{\left (x + 1 \right )} - \frac{5 \log{\left (x + 2 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-3+x)/(x**3+3*x**2+2*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00860018, size = 21, normalized size = 1. \[ -\frac{3 \log (x)}{2}+4 \log (x+1)-\frac{5}{2} \log (x+2) \]
Antiderivative was successfully verified.
[In] Integrate[(-3 + x)/(2*x + 3*x^2 + x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 18, normalized size = 0.9 \[ -{\frac{3\,\ln \left ( x \right ) }{2}}+4\,\ln \left ( 1+x \right ) -{\frac{5\,\ln \left ( 2+x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-3+x)/(x^3+3*x^2+2*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.785245, size = 23, normalized size = 1.1 \[ -\frac{5}{2} \, \log \left (x + 2\right ) + 4 \, \log \left (x + 1\right ) - \frac{3}{2} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x - 3)/(x^3 + 3*x^2 + 2*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.271498, size = 23, normalized size = 1.1 \[ -\frac{5}{2} \, \log \left (x + 2\right ) + 4 \, \log \left (x + 1\right ) - \frac{3}{2} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x - 3)/(x^3 + 3*x^2 + 2*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.275557, size = 20, normalized size = 0.95 \[ - \frac{3 \log{\left (x \right )}}{2} + 4 \log{\left (x + 1 \right )} - \frac{5 \log{\left (x + 2 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3+x)/(x**3+3*x**2+2*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.259774, size = 27, normalized size = 1.29 \[ -\frac{5}{2} \,{\rm ln}\left ({\left | x + 2 \right |}\right ) + 4 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) - \frac{3}{2} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x - 3)/(x^3 + 3*x^2 + 2*x),x, algorithm="giac")
[Out]