Optimal. Leaf size=52 \[ -\frac{200 x^3}{81}+\frac{230 x^2}{27}-\frac{1546 x}{81}+\frac{3724}{729 (3 x+2)}-\frac{343}{1458 (3 x+2)^2}+\frac{11599}{729} \log (3 x+2) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0646062, antiderivative size = 52, 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 \[ -\frac{200 x^3}{81}+\frac{230 x^2}{27}-\frac{1546 x}{81}+\frac{3724}{729 (3 x+2)}-\frac{343}{1458 (3 x+2)^2}+\frac{11599}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{200 x^{3}}{81} + \frac{11599 \log{\left (3 x + 2 \right )}}{729} + \int \left (- \frac{1546}{81}\right )\, dx + \frac{460 \int x\, dx}{27} + \frac{3724}{729 \left (3 x + 2\right )} - \frac{343}{1458 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0529053, size = 51, normalized size = 0.98 \[ -\frac{97200 x^5-205740 x^4+347436 x^3+1531512 x^2+1171896 x-69594 (3 x+2)^2 \log (30 x+20)+258005}{4374 (3 x+2)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 41, normalized size = 0.8 \[ -{\frac{1546\,x}{81}}+{\frac{230\,{x}^{2}}{27}}-{\frac{200\,{x}^{3}}{81}}-{\frac{343}{1458\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{3724}{1458+2187\,x}}+{\frac{11599\,\ln \left ( 2+3\,x \right ) }{729}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(3+5*x)^2/(2+3*x)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34561, size = 55, normalized size = 1.06 \[ -\frac{200}{81} \, x^{3} + \frac{230}{27} \, x^{2} - \frac{1546}{81} \, x + \frac{49 \,{\left (152 \, x + 99\right )}}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{11599}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.209218, size = 77, normalized size = 1.48 \[ -\frac{32400 \, x^{5} - 68580 \, x^{4} + 115812 \, x^{3} + 284256 \, x^{2} - 23198 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 88968 \, x - 14553}{1458 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.296302, size = 42, normalized size = 0.81 \[ - \frac{200 x^{3}}{81} + \frac{230 x^{2}}{27} - \frac{1546 x}{81} + \frac{7448 x + 4851}{4374 x^{2} + 5832 x + 1944} + \frac{11599 \log{\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208718, size = 50, normalized size = 0.96 \[ -\frac{200}{81} \, x^{3} + \frac{230}{27} \, x^{2} - \frac{1546}{81} \, x + \frac{49 \,{\left (152 \, x + 99\right )}}{486 \,{\left (3 \, x + 2\right )}^{2}} + \frac{11599}{729} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^3,x, algorithm="giac")
[Out]