3.1252 \(\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=56 \[ -\frac{100}{729 (3 x+2)^3}+\frac{185}{243 (3 x+2)^4}-\frac{503}{405 (3 x+2)^5}+\frac{259}{729 (3 x+2)^6}-\frac{7}{243 (3 x+2)^7} \]

[Out]

-7/(243*(2 + 3*x)^7) + 259/(729*(2 + 3*x)^6) - 503/(405*(2 + 3*x)^5) + 185/(243*
(2 + 3*x)^4) - 100/(729*(2 + 3*x)^3)

_______________________________________________________________________________________

Rubi [A]  time = 0.061958, antiderivative size = 56, 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 \[ -\frac{100}{729 (3 x+2)^3}+\frac{185}{243 (3 x+2)^4}-\frac{503}{405 (3 x+2)^5}+\frac{259}{729 (3 x+2)^6}-\frac{7}{243 (3 x+2)^7} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^8,x]

[Out]

-7/(243*(2 + 3*x)^7) + 259/(729*(2 + 3*x)^6) - 503/(405*(2 + 3*x)^5) + 185/(243*
(2 + 3*x)^4) - 100/(729*(2 + 3*x)^3)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 10.1682, size = 49, normalized size = 0.88 \[ - \frac{100}{729 \left (3 x + 2\right )^{3}} + \frac{185}{243 \left (3 x + 2\right )^{4}} - \frac{503}{405 \left (3 x + 2\right )^{5}} + \frac{259}{729 \left (3 x + 2\right )^{6}} - \frac{7}{243 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**8,x)

[Out]

-100/(729*(3*x + 2)**3) + 185/(243*(3*x + 2)**4) - 503/(405*(3*x + 2)**5) + 259/
(729*(3*x + 2)**6) - 7/(243*(3*x + 2)**7)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0206623, size = 31, normalized size = 0.55 \[ \frac{-40500 x^4-33075 x^3+1107 x^2+1461 x-1423}{3645 (3 x+2)^7} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^8,x]

[Out]

(-1423 + 1461*x + 1107*x^2 - 33075*x^3 - 40500*x^4)/(3645*(2 + 3*x)^7)

_______________________________________________________________________________________

Maple [A]  time = 0.007, size = 47, normalized size = 0.8 \[ -{\frac{7}{243\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{259}{729\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{503}{405\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{185}{243\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{100}{729\, \left ( 2+3\,x \right ) ^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(3+5*x)^2/(2+3*x)^8,x)

[Out]

-7/243/(2+3*x)^7+259/729/(2+3*x)^6-503/405/(2+3*x)^5+185/243/(2+3*x)^4-100/729/(
2+3*x)^3

_______________________________________________________________________________________

Maxima [A]  time = 1.3508, size = 80, normalized size = 1.43 \[ -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^8,x, algorithm="maxima")

[Out]

-1/3645*(40500*x^4 + 33075*x^3 - 1107*x^2 - 1461*x + 1423)/(2187*x^7 + 10206*x^6
+ 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

_______________________________________________________________________________________

Fricas [A]  time = 0.198245, size = 80, normalized size = 1.43 \[ -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^8,x, algorithm="fricas")

[Out]

-1/3645*(40500*x^4 + 33075*x^3 - 1107*x^2 - 1461*x + 1423)/(2187*x^7 + 10206*x^6
+ 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

_______________________________________________________________________________________

Sympy [A]  time = 0.486955, size = 56, normalized size = 1. \[ - \frac{40500 x^{4} + 33075 x^{3} - 1107 x^{2} - 1461 x + 1423}{7971615 x^{7} + 37200870 x^{6} + 74401740 x^{5} + 82668600 x^{4} + 55112400 x^{3} + 22044960 x^{2} + 4898880 x + 466560} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**8,x)

[Out]

-(40500*x**4 + 33075*x**3 - 1107*x**2 - 1461*x + 1423)/(7971615*x**7 + 37200870*
x**6 + 74401740*x**5 + 82668600*x**4 + 55112400*x**3 + 22044960*x**2 + 4898880*x
+ 466560)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.206224, size = 39, normalized size = 0.7 \[ -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\left (3 \, x + 2\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^8,x, algorithm="giac")

[Out]

-1/3645*(40500*x^4 + 33075*x^3 - 1107*x^2 - 1461*x + 1423)/(3*x + 2)^7