Optimal. Leaf size=34 \[ -\frac{9 x^2}{25}+\frac{33 x}{125}-\frac{11}{625 (5 x+3)}+\frac{64}{625} \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0448879, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{9 x^2}{25}+\frac{33 x}{125}-\frac{11}{625 (5 x+3)}+\frac{64}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{64 \log{\left (5 x + 3 \right )}}{625} + \int \frac{33}{125}\, dx - \frac{18 \int x\, dx}{25} - \frac{11}{625 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)**2/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0201884, size = 41, normalized size = 1.21 \[ \frac{-1125 x^3+150 x^2+1545 x+64 (5 x+3) \log (-3 (5 x+3))+619}{625 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 27, normalized size = 0.8 \[{\frac{33\,x}{125}}-{\frac{9\,{x}^{2}}{25}}-{\frac{11}{1875+3125\,x}}+{\frac{64\,\ln \left ( 3+5\,x \right ) }{625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)^2/(3+5*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34209, size = 35, normalized size = 1.03 \[ -\frac{9}{25} \, x^{2} + \frac{33}{125} \, x - \frac{11}{625 \,{\left (5 \, x + 3\right )}} + \frac{64}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)/(5*x + 3)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218293, size = 50, normalized size = 1.47 \[ -\frac{1125 \, x^{3} - 150 \, x^{2} - 64 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 495 \, x + 11}{625 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)/(5*x + 3)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.199334, size = 27, normalized size = 0.79 \[ - \frac{9 x^{2}}{25} + \frac{33 x}{125} + \frac{64 \log{\left (5 x + 3 \right )}}{625} - \frac{11}{3125 x + 1875} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)**2/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212051, size = 65, normalized size = 1.91 \[ \frac{3}{625} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{29}{5 \, x + 3} - 3\right )} - \frac{11}{625 \,{\left (5 \, x + 3\right )}} - \frac{64}{625} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)/(5*x + 3)^2,x, algorithm="giac")
[Out]