Optimal. Leaf size=43 \[ -\frac{217}{484 (1-2 x)}+\frac{49}{88 (1-2 x)^2}-\frac{\log (1-2 x)}{1331}+\frac{\log (5 x+3)}{1331} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0533031, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{217}{484 (1-2 x)}+\frac{49}{88 (1-2 x)^2}-\frac{\log (1-2 x)}{1331}+\frac{\log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.80552, size = 32, normalized size = 0.74 \[ - \frac{\log{\left (- 2 x + 1 \right )}}{1331} + \frac{\log{\left (5 x + 3 \right )}}{1331} - \frac{217}{484 \left (- 2 x + 1\right )} + \frac{49}{88 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2/(1-2*x)**3/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0344692, size = 35, normalized size = 0.81 \[ \frac{\frac{77 (124 x+15)}{(1-2 x)^2}-8 \log (5-10 x)+8 \log (5 x+3)}{10648} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.011, size = 36, normalized size = 0.8 \[{\frac{\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{49}{88\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{217}{-484+968\,x}}-{\frac{\ln \left ( -1+2\,x \right ) }{1331}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2/(1-2*x)^3/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35282, size = 49, normalized size = 1.14 \[ \frac{7 \,{\left (124 \, x + 15\right )}}{968 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{1331} \, \log \left (5 \, x + 3\right ) - \frac{1}{1331} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2/((5*x + 3)*(2*x - 1)^3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.210507, size = 74, normalized size = 1.72 \[ \frac{8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 9548 \, x + 1155}{10648 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2/((5*x + 3)*(2*x - 1)^3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.34326, size = 31, normalized size = 0.72 \[ \frac{868 x + 105}{3872 x^{2} - 3872 x + 968} - \frac{\log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{\log{\left (x + \frac{3}{5} \right )}}{1331} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2/(1-2*x)**3/(3+5*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.224847, size = 45, normalized size = 1.05 \[ \frac{7 \,{\left (124 \, x + 15\right )}}{968 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1}{1331} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2/((5*x + 3)*(2*x - 1)^3),x, algorithm="giac")
[Out]