3.1232 \(\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^5} \, dx\)

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]

(1 - 2*x)^3/(84*(2 + 3*x)^4) - (23*(1 - 2*x)^3)/(294*(2 + 3*x)^3)

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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]

(1 - 2*x)^3/(84*(2 + 3*x)^4) - (23*(1 - 2*x)^3)/(294*(2 + 3*x)^3)

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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]

-23*(-2*x + 1)**3/(294*(3*x + 2)**3) + (-2*x + 1)**3/(84*(3*x + 2)**4)

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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]

-(167 + 516*x + 1728*x^2 + 2160*x^3)/(324*(2 + 3*x)^4)

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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]

-20/81/(2+3*x)-91/81/(2+3*x)^3+49/324/(2+3*x)^4+8/9/(2+3*x)^2

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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]

-1/324*(2160*x^3 + 1728*x^2 + 516*x + 167)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x +
16)

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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]

-1/324*(2160*x^3 + 1728*x^2 + 516*x + 167)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x +
16)

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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]

-(2160*x**3 + 1728*x**2 + 516*x + 167)/(26244*x**4 + 69984*x**3 + 69984*x**2 + 3
1104*x + 5184)

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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]

-20/81/(3*x + 2) + 8/9/(3*x + 2)^2 - 91/81/(3*x + 2)^3 + 49/324/(3*x + 2)^4