Optimal. Leaf size=34 \[ \frac{75 x^2}{8}+\frac{215 x}{4}+\frac{847}{16 (1-2 x)}+\frac{1133}{16} \log (1-2 x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0457221, 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 \[ \frac{75 x^2}{8}+\frac{215 x}{4}+\frac{847}{16 (1-2 x)}+\frac{1133}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{1133 \log{\left (- 2 x + 1 \right )}}{16} + \int \frac{215}{4}\, dx + \frac{75 \int x\, dx}{4} + \frac{847}{16 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)*(3+5*x)**2/(1-2*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0170445, size = 36, normalized size = 1.06 \[ \frac{600 x^3+3140 x^2-3590 x+2266 (2 x-1) \log (1-2 x)-759}{64 x-32} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 27, normalized size = 0.8 \[{\frac{75\,{x}^{2}}{8}}+{\frac{215\,x}{4}}-{\frac{847}{-16+32\,x}}+{\frac{1133\,\ln \left ( -1+2\,x \right ) }{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)*(3+5*x)^2/(1-2*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35574, size = 35, normalized size = 1.03 \[ \frac{75}{8} \, x^{2} + \frac{215}{4} \, x - \frac{847}{16 \,{\left (2 \, x - 1\right )}} + \frac{1133}{16} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)/(2*x - 1)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.199545, size = 50, normalized size = 1.47 \[ \frac{300 \, x^{3} + 1570 \, x^{2} + 1133 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 860 \, x - 847}{16 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)/(2*x - 1)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.195006, size = 27, normalized size = 0.79 \[ \frac{75 x^{2}}{8} + \frac{215 x}{4} + \frac{1133 \log{\left (2 x - 1 \right )}}{16} - \frac{847}{32 x - 16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)*(3+5*x)**2/(1-2*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.220286, size = 65, normalized size = 1.91 \[ \frac{5}{32} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{202}{2 \, x - 1} + 15\right )} - \frac{847}{16 \,{\left (2 \, x - 1\right )}} - \frac{1133}{16} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)/(2*x - 1)^2,x, algorithm="giac")
[Out]