Optimal. Leaf size=46 \[ \frac{49}{3 x+2}+\frac{154}{5 x+3}-\frac{121}{10 (5 x+3)^2}-707 \log (3 x+2)+707 \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0593245, antiderivative size = 46, 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 \[ \frac{49}{3 x+2}+\frac{154}{5 x+3}-\frac{121}{10 (5 x+3)^2}-707 \log (3 x+2)+707 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 8.43101, size = 39, normalized size = 0.85 \[ - 707 \log{\left (3 x + 2 \right )} + 707 \log{\left (5 x + 3 \right )} + \frac{154}{5 x + 3} - \frac{121}{10 \left (5 x + 3\right )^{2}} + \frac{49}{3 x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**2/(3+5*x)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0428313, size = 48, normalized size = 1.04 \[ \frac{49}{3 x+2}+\frac{154}{5 x+3}-\frac{121}{10 (5 x+3)^2}-707 \log (5 (3 x+2))+707 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 45, normalized size = 1. \[ 49\, \left ( 2+3\,x \right ) ^{-1}-{\frac{121}{10\, \left ( 3+5\,x \right ) ^{2}}}+154\, \left ( 3+5\,x \right ) ^{-1}-707\,\ln \left ( 2+3\,x \right ) +707\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^2/(3+5*x)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33123, size = 62, normalized size = 1.35 \[ \frac{35350 \, x^{2} + 43597 \, x + 13408}{10 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 707 \, \log \left (5 \, x + 3\right ) - 707 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.210618, size = 101, normalized size = 2.2 \[ \frac{35350 \, x^{2} + 7070 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 7070 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 43597 \, x + 13408}{10 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.384152, size = 41, normalized size = 0.89 \[ \frac{35350 x^{2} + 43597 x + 13408}{750 x^{3} + 1400 x^{2} + 870 x + 180} + 707 \log{\left (x + \frac{3}{5} \right )} - 707 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**2/(3+5*x)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212975, size = 66, normalized size = 1.43 \[ \frac{49}{3 \, x + 2} - \frac{33 \,{\left (\frac{206}{3 \, x + 2} - 865\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + 707 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="giac")
[Out]