3.1335 \(\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^6} \, dx\)

Optimal. Leaf size=37 \[ \frac{(1-2 x)^4}{105 (3 x+2)^5}-\frac{173 (1-2 x)^4}{2940 (3 x+2)^4} \]

[Out]

(1 - 2*x)^4/(105*(2 + 3*x)^5) - (173*(1 - 2*x)^4)/(2940*(2 + 3*x)^4)

_______________________________________________________________________________________

Rubi [A]  time = 0.0368793, 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 \[ \frac{(1-2 x)^4}{105 (3 x+2)^5}-\frac{173 (1-2 x)^4}{2940 (3 x+2)^4} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^6,x]

[Out]

(1 - 2*x)^4/(105*(2 + 3*x)^5) - (173*(1 - 2*x)^4)/(2940*(2 + 3*x)^4)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 5.29486, size = 31, normalized size = 0.84 \[ - \frac{173 \left (- 2 x + 1\right )^{4}}{2940 \left (3 x + 2\right )^{4}} + \frac{\left (- 2 x + 1\right )^{4}}{105 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(3+5*x)/(2+3*x)**6,x)

[Out]

-173*(-2*x + 1)**4/(2940*(3*x + 2)**4) + (-2*x + 1)**4/(105*(3*x + 2)**5)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0183453, size = 31, normalized size = 0.84 \[ \frac{64800 x^4+57240 x^3+34920 x^2+16905 x+1282}{4860 (3 x+2)^5} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^6,x]

[Out]

(1282 + 16905*x + 34920*x^2 + 57240*x^3 + 64800*x^4)/(4860*(2 + 3*x)^5)

_______________________________________________________________________________________

Maple [A]  time = 0.008, size = 47, normalized size = 1.3 \[{\frac{343}{1215\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{40}{486+729\,x}}+{\frac{518}{243\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{2009}{972\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{214}{243\, \left ( 2+3\,x \right ) ^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(3+5*x)/(2+3*x)^6,x)

[Out]

343/1215/(2+3*x)^5+40/243/(2+3*x)+518/243/(2+3*x)^3-2009/972/(2+3*x)^4-214/243/(
2+3*x)^2

_______________________________________________________________________________________

Maxima [A]  time = 1.35065, size = 66, normalized size = 1.78 \[ \frac{64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="maxima")

[Out]

1/4860*(64800*x^4 + 57240*x^3 + 34920*x^2 + 16905*x + 1282)/(243*x^5 + 810*x^4 +
1080*x^3 + 720*x^2 + 240*x + 32)

_______________________________________________________________________________________

Fricas [A]  time = 0.21043, size = 66, normalized size = 1.78 \[ \frac{64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="fricas")

[Out]

1/4860*(64800*x^4 + 57240*x^3 + 34920*x^2 + 16905*x + 1282)/(243*x^5 + 810*x^4 +
1080*x^3 + 720*x^2 + 240*x + 32)

_______________________________________________________________________________________

Sympy [A]  time = 0.387362, size = 44, normalized size = 1.19 \[ \frac{64800 x^{4} + 57240 x^{3} + 34920 x^{2} + 16905 x + 1282}{1180980 x^{5} + 3936600 x^{4} + 5248800 x^{3} + 3499200 x^{2} + 1166400 x + 155520} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(3+5*x)/(2+3*x)**6,x)

[Out]

(64800*x**4 + 57240*x**3 + 34920*x**2 + 16905*x + 1282)/(1180980*x**5 + 3936600*
x**4 + 5248800*x**3 + 3499200*x**2 + 1166400*x + 155520)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.211088, size = 39, normalized size = 1.05 \[ \frac{64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \,{\left (3 \, x + 2\right )}^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="giac")

[Out]

1/4860*(64800*x^4 + 57240*x^3 + 34920*x^2 + 16905*x + 1282)/(3*x + 2)^5