3.1234 \(\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx\)

Optimal. Leaf size=45 \[ -\frac{20}{243 (3 x+2)^3}+\frac{4}{9 (3 x+2)^4}-\frac{91}{135 (3 x+2)^5}+\frac{49}{486 (3 x+2)^6} \]

[Out]

49/(486*(2 + 3*x)^6) - 91/(135*(2 + 3*x)^5) + 4/(9*(2 + 3*x)^4) - 20/(243*(2 + 3
*x)^3)

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Rubi [A]  time = 0.0480717, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{20}{243 (3 x+2)^3}+\frac{4}{9 (3 x+2)^4}-\frac{91}{135 (3 x+2)^5}+\frac{49}{486 (3 x+2)^6} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^7,x]

[Out]

49/(486*(2 + 3*x)^6) - 91/(135*(2 + 3*x)^5) + 4/(9*(2 + 3*x)^4) - 20/(243*(2 + 3
*x)^3)

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Rubi in Sympy [A]  time = 8.17168, size = 39, normalized size = 0.87 \[ - \frac{20}{243 \left (3 x + 2\right )^{3}} + \frac{4}{9 \left (3 x + 2\right )^{4}} - \frac{91}{135 \left (3 x + 2\right )^{5}} + \frac{49}{486 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(3+5*x)/(2+3*x)**7,x)

[Out]

-20/(243*(3*x + 2)**3) + 4/(9*(3*x + 2)**4) - 91/(135*(3*x + 2)**5) + 49/(486*(3
*x + 2)**6)

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Mathematica [A]  time = 0.0173274, size = 26, normalized size = 0.58 \[ -\frac{5400 x^3+1080 x^2-846 x+311}{2430 (3 x+2)^6} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^7,x]

[Out]

-(311 - 846*x + 1080*x^2 + 5400*x^3)/(2430*(2 + 3*x)^6)

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Maple [A]  time = 0.008, size = 38, normalized size = 0.8 \[{\frac{49}{486\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{91}{135\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{4}{9\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{20}{243\, \left ( 2+3\,x \right ) ^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(3+5*x)/(2+3*x)^7,x)

[Out]

49/486/(2+3*x)^6-91/135/(2+3*x)^5+4/9/(2+3*x)^4-20/243/(2+3*x)^3

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Maxima [A]  time = 1.35069, size = 66, normalized size = 1.47 \[ -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="maxima")

[Out]

-1/2430*(5400*x^3 + 1080*x^2 - 846*x + 311)/(729*x^6 + 2916*x^5 + 4860*x^4 + 432
0*x^3 + 2160*x^2 + 576*x + 64)

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Fricas [A]  time = 0.198218, size = 66, normalized size = 1.47 \[ -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="fricas")

[Out]

-1/2430*(5400*x^3 + 1080*x^2 - 846*x + 311)/(729*x^6 + 2916*x^5 + 4860*x^4 + 432
0*x^3 + 2160*x^2 + 576*x + 64)

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Sympy [A]  time = 0.419933, size = 46, normalized size = 1.02 \[ - \frac{5400 x^{3} + 1080 x^{2} - 846 x + 311}{1771470 x^{6} + 7085880 x^{5} + 11809800 x^{4} + 10497600 x^{3} + 5248800 x^{2} + 1399680 x + 155520} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(3+5*x)/(2+3*x)**7,x)

[Out]

-(5400*x**3 + 1080*x**2 - 846*x + 311)/(1771470*x**6 + 7085880*x**5 + 11809800*x
**4 + 10497600*x**3 + 5248800*x**2 + 1399680*x + 155520)

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GIAC/XCAS [A]  time = 0.206, size = 32, normalized size = 0.71 \[ -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (3 \, x + 2\right )}^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="giac")

[Out]

-1/2430*(5400*x^3 + 1080*x^2 - 846*x + 311)/(3*x + 2)^6