Optimal. Leaf size=39 \[ \frac{217}{9 (3 x+2)}+\frac{49}{18 (3 x+2)^2}-121 \log (3 x+2)+121 \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0487158, antiderivative size = 39, 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 \[ \frac{217}{9 (3 x+2)}+\frac{49}{18 (3 x+2)^2}-121 \log (3 x+2)+121 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.31661, size = 32, normalized size = 0.82 \[ - 121 \log{\left (3 x + 2 \right )} + 121 \log{\left (5 x + 3 \right )} + \frac{217}{9 \left (3 x + 2\right )} + \frac{49}{18 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**3/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.027363, size = 48, normalized size = 1.23 \[ \frac{1302 x-2178 (3 x+2)^2 \log (5 (3 x+2))+2178 (3 x+2)^2 \log (5 x+3)+917}{18 (3 x+2)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.011, size = 36, normalized size = 0.9 \[{\frac{49}{18\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{217}{18+27\,x}}-121\,\ln \left ( 2+3\,x \right ) +121\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^3/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34989, size = 49, normalized size = 1.26 \[ \frac{7 \,{\left (186 \, x + 131\right )}}{18 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + 121 \, \log \left (5 \, x + 3\right ) - 121 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.219863, size = 74, normalized size = 1.9 \[ \frac{2178 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 2178 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 1302 \, x + 917}{18 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.345516, size = 31, normalized size = 0.79 \[ \frac{1302 x + 917}{162 x^{2} + 216 x + 72} + 121 \log{\left (x + \frac{3}{5} \right )} - 121 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**3/(3+5*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.220449, size = 45, normalized size = 1.15 \[ \frac{7 \,{\left (186 \, x + 131\right )}}{18 \,{\left (3 \, x + 2\right )}^{2}} + 121 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 121 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^3),x, algorithm="giac")
[Out]