Optimal. Leaf size=65 \[ \frac{1331}{2401 (1-2 x)}+\frac{363}{2401 (3 x+2)}-\frac{101}{6174 (3 x+2)^2}+\frac{1}{1323 (3 x+2)^3}-\frac{3267 \log (1-2 x)}{16807}+\frac{3267 \log (3 x+2)}{16807} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0734643, antiderivative size = 65, 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 \[ \frac{1331}{2401 (1-2 x)}+\frac{363}{2401 (3 x+2)}-\frac{101}{6174 (3 x+2)^2}+\frac{1}{1323 (3 x+2)^3}-\frac{3267 \log (1-2 x)}{16807}+\frac{3267 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.2391, size = 53, normalized size = 0.82 \[ - \frac{3267 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{3267 \log{\left (3 x + 2 \right )}}{16807} + \frac{363}{2401 \left (3 x + 2\right )} - \frac{101}{6174 \left (3 x + 2\right )^{2}} + \frac{1}{1323 \left (3 x + 2\right )^{3}} + \frac{1331}{2401 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)**2/(2+3*x)**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0682914, size = 62, normalized size = 0.95 \[ \frac{\frac{7}{2} \left (\frac{19602}{3 x+2}-\frac{2121}{(3 x+2)^2}+\frac{98}{(3 x+2)^3}+\frac{71874}{1-2 x}\right )-88209 \log (1-2 x)+88209 \log (6 x+4)}{453789} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.015, size = 54, normalized size = 0.8 \[{\frac{1}{1323\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{101}{6174\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{363}{4802+7203\,x}}+{\frac{3267\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{1331}{-2401+4802\,x}}-{\frac{3267\,\ln \left ( -1+2\,x \right ) }{16807}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)^2/(2+3*x)^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34891, size = 76, normalized size = 1.17 \[ -\frac{1587762 \, x^{3} + 3599892 \, x^{2} + 2667797 \, x + 649256}{129654 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac{3267}{16807} \, \log \left (3 \, x + 2\right ) - \frac{3267}{16807} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.214723, size = 128, normalized size = 1.97 \[ -\frac{11114334 \, x^{3} + 25199244 \, x^{2} - 176418 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 176418 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 18674579 \, x + 4544792}{907578 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.448139, size = 54, normalized size = 0.83 \[ - \frac{1587762 x^{3} + 3599892 x^{2} + 2667797 x + 649256}{7001316 x^{4} + 10501974 x^{3} + 2333772 x^{2} - 2593080 x - 1037232} - \frac{3267 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{3267 \log{\left (x + \frac{2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**3/(1-2*x)**2/(2+3*x)**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.20895, size = 81, normalized size = 1.25 \[ -\frac{1331}{2401 \,{\left (2 \, x - 1\right )}} - \frac{2 \,{\left (\frac{43645}{2 \, x - 1} + \frac{50127}{{\left (2 \, x - 1\right )}^{2}} + 9502\right )}}{16807 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} + \frac{3267}{16807} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^4*(2*x - 1)^2),x, algorithm="giac")
[Out]