Optimal. Leaf size=37 \[ \frac{(1-2 x)^3}{84 (3 x+2)^4}-\frac{23 (1-2 x)^3}{294 (3 x+2)^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0360346, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{(1-2 x)^3}{84 (3 x+2)^4}-\frac{23 (1-2 x)^3}{294 (3 x+2)^3} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.27634, size = 31, normalized size = 0.84 \[ - \frac{23 \left (- 2 x + 1\right )^{3}}{294 \left (3 x + 2\right )^{3}} + \frac{\left (- 2 x + 1\right )^{3}}{84 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)/(2+3*x)**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.017424, size = 26, normalized size = 0.7 \[ -\frac{2160 x^3+1728 x^2+516 x+167}{324 (3 x+2)^4} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 38, normalized size = 1. \[ -{\frac{20}{162+243\,x}}-{\frac{91}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{49}{324\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{8}{9\, \left ( 2+3\,x \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)/(2+3*x)^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35789, size = 53, normalized size = 1.43 \[ -\frac{2160 \, x^{3} + 1728 \, x^{2} + 516 \, x + 167}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.209842, size = 53, normalized size = 1.43 \[ -\frac{2160 \, x^{3} + 1728 \, x^{2} + 516 \, x + 167}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.343918, size = 36, normalized size = 0.97 \[ - \frac{2160 x^{3} + 1728 x^{2} + 516 x + 167}{26244 x^{4} + 69984 x^{3} + 69984 x^{2} + 31104 x + 5184} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)/(2+3*x)**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.206653, size = 50, normalized size = 1.35 \[ -\frac{20}{81 \,{\left (3 \, x + 2\right )}} + \frac{8}{9 \,{\left (3 \, x + 2\right )}^{2}} - \frac{91}{81 \,{\left (3 \, x + 2\right )}^{3}} + \frac{49}{324 \,{\left (3 \, x + 2\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^5,x, algorithm="giac")
[Out]