Optimal. Leaf size=67 \[ \frac{100}{729 (3 x+2)^2}-\frac{2180}{2187 (3 x+2)^3}+\frac{4099}{1458 (3 x+2)^4}-\frac{11599}{3645 (3 x+2)^5}+\frac{1862}{2187 (3 x+2)^6}-\frac{49}{729 (3 x+2)^7} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0716052, 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 \[ \frac{100}{729 (3 x+2)^2}-\frac{2180}{2187 (3 x+2)^3}+\frac{4099}{1458 (3 x+2)^4}-\frac{11599}{3645 (3 x+2)^5}+\frac{1862}{2187 (3 x+2)^6}-\frac{49}{729 (3 x+2)^7} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^8,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.5506, size = 60, normalized size = 0.9 \[ \frac{100}{729 \left (3 x + 2\right )^{2}} - \frac{2180}{2187 \left (3 x + 2\right )^{3}} + \frac{4099}{1458 \left (3 x + 2\right )^{4}} - \frac{11599}{3645 \left (3 x + 2\right )^{5}} + \frac{1862}{2187 \left (3 x + 2\right )^{6}} - \frac{49}{729 \left (3 x + 2\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**8,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0412548, size = 36, normalized size = 0.54 \[ \frac{729000 x^5+664200 x^4+191295 x^3+145044 x^2+61392 x-3526}{21870 (3 x+2)^7} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^8,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 56, normalized size = 0.8 \[ -{\frac{49}{729\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{1862}{2187\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{11599}{3645\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{4099}{1458\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{2180}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{100}{729\, \left ( 2+3\,x \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(3+5*x)^2/(2+3*x)^8,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34967, size = 86, normalized size = 1.28 \[ \frac{729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^8,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.19475, size = 86, normalized size = 1.28 \[ \frac{729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^8,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.526282, size = 60, normalized size = 0.9 \[ \frac{729000 x^{5} + 664200 x^{4} + 191295 x^{3} + 145044 x^{2} + 61392 x - 3526}{47829690 x^{7} + 223205220 x^{6} + 446410440 x^{5} + 496011600 x^{4} + 330674400 x^{3} + 132269760 x^{2} + 29393280 x + 2799360} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**8,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210854, size = 46, normalized size = 0.69 \[ \frac{729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \,{\left (3 \, x + 2\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^8,x, algorithm="giac")
[Out]