Optimal. Leaf size=67 \[ -\frac{500}{729 (3 x+2)}+\frac{1900}{729 (3 x+2)^2}-\frac{8285}{2187 (3 x+2)^3}+\frac{4099}{2916 (3 x+2)^4}-\frac{763}{3645 (3 x+2)^5}+\frac{49}{4374 (3 x+2)^6} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.068741, antiderivative size = 67, 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 \[ -\frac{500}{729 (3 x+2)}+\frac{1900}{729 (3 x+2)^2}-\frac{8285}{2187 (3 x+2)^3}+\frac{4099}{2916 (3 x+2)^4}-\frac{763}{3645 (3 x+2)^5}+\frac{49}{4374 (3 x+2)^6} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^7,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.4704, size = 56, normalized size = 0.84 \[ - \frac{500}{729 \left (3 x + 2\right )} + \frac{1900}{729 \left (3 x + 2\right )^{2}} - \frac{8285}{2187 \left (3 x + 2\right )^{3}} + \frac{4099}{2916 \left (3 x + 2\right )^{4}} - \frac{763}{3645 \left (3 x + 2\right )^{5}} + \frac{49}{4374 \left (3 x + 2\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)**3/(2+3*x)**7,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0433932, size = 36, normalized size = 0.54 \[ -\frac{7290000 x^5+15066000 x^4+12249900 x^3+5370435 x^2+1510848 x+233482}{43740 (3 x+2)^6} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^7,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 56, normalized size = 0.8 \[{\frac{49}{4374\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{763}{3645\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{4099}{2916\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{8285}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1900}{729\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{500}{1458+2187\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)^3/(2+3*x)^7,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35184, size = 80, normalized size = 1.19 \[ -\frac{7290000 \, x^{5} + 15066000 \, x^{4} + 12249900 \, x^{3} + 5370435 \, x^{2} + 1510848 \, x + 233482}{43740 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.198869, size = 80, normalized size = 1.19 \[ -\frac{7290000 \, x^{5} + 15066000 \, x^{4} + 12249900 \, x^{3} + 5370435 \, x^{2} + 1510848 \, x + 233482}{43740 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.459681, size = 56, normalized size = 0.84 \[ - \frac{7290000 x^{5} + 15066000 x^{4} + 12249900 x^{3} + 5370435 x^{2} + 1510848 x + 233482}{31886460 x^{6} + 127545840 x^{5} + 212576400 x^{4} + 188956800 x^{3} + 94478400 x^{2} + 25194240 x + 2799360} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)**3/(2+3*x)**7,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.211114, size = 46, normalized size = 0.69 \[ -\frac{7290000 \, x^{5} + 15066000 \, x^{4} + 12249900 \, x^{3} + 5370435 \, x^{2} + 1510848 \, x + 233482}{43740 \,{\left (3 \, x + 2\right )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="giac")
[Out]