3.1154 \(\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx\)

Optimal. Leaf size=37 \[ \frac{3 (5 x+3)^3}{4 (3 x+2)^3}+\frac{7 (5 x+3)^3}{12 (3 x+2)^4} \]

[Out]

(7*(3 + 5*x)^3)/(12*(2 + 3*x)^4) + (3*(3 + 5*x)^3)/(4*(2 + 3*x)^3)

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Rubi [A]  time = 0.0352916, 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 \[ \frac{3 (5 x+3)^3}{4 (3 x+2)^3}+\frac{7 (5 x+3)^3}{12 (3 x+2)^4} \]

Antiderivative was successfully verified.

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

[Out]

(7*(3 + 5*x)^3)/(12*(2 + 3*x)^4) + (3*(3 + 5*x)^3)/(4*(2 + 3*x)^3)

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Rubi in Sympy [A]  time = 5.42282, size = 32, normalized size = 0.86 \[ \frac{3 \left (5 x + 3\right )^{3}}{4 \left (3 x + 2\right )^{3}} + \frac{7 \left (5 x + 3\right )^{3}}{12 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*(5*x + 3)**3/(4*(3*x + 2)**3) + 7*(5*x + 3)**3/(12*(3*x + 2)**4)

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Mathematica [A]  time = 0.0150034, size = 26, normalized size = 0.7 \[ \frac{600 x^3+810 x^2+312 x+25}{36 (3 x+2)^4} \]

Antiderivative was successfully verified.

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

[Out]

(25 + 312*x + 810*x^2 + 600*x^3)/(36*(2 + 3*x)^4)

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Maple [A]  time = 0.008, size = 38, normalized size = 1. \[{\frac{50}{162+243\,x}}+{\frac{8}{27\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{7}{324\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{65}{54\, \left ( 2+3\,x \right ) ^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50/81/(2+3*x)+8/27/(2+3*x)^3-7/324/(2+3*x)^4-65/54/(2+3*x)^2

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Maxima [A]  time = 1.35013, size = 53, normalized size = 1.43 \[ \frac{600 \, x^{3} + 810 \, x^{2} + 312 \, x + 25}{36 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/36*(600*x^3 + 810*x^2 + 312*x + 25)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Fricas [A]  time = 0.208966, size = 53, normalized size = 1.43 \[ \frac{600 \, x^{3} + 810 \, x^{2} + 312 \, x + 25}{36 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/36*(600*x^3 + 810*x^2 + 312*x + 25)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Sympy [A]  time = 0.330186, size = 34, normalized size = 0.92 \[ \frac{600 x^{3} + 810 x^{2} + 312 x + 25}{2916 x^{4} + 7776 x^{3} + 7776 x^{2} + 3456 x + 576} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(600*x**3 + 810*x**2 + 312*x + 25)/(2916*x**4 + 7776*x**3 + 7776*x**2 + 3456*x +
576)

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GIAC/XCAS [A]  time = 0.210853, size = 50, normalized size = 1.35 \[ \frac{50}{81 \,{\left (3 \, x + 2\right )}} - \frac{65}{54 \,{\left (3 \, x + 2\right )}^{2}} + \frac{8}{27 \,{\left (3 \, x + 2\right )}^{3}} - \frac{7}{324 \,{\left (3 \, x + 2\right )}^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50/81/(3*x + 2) - 65/54/(3*x + 2)^2 + 8/27/(3*x + 2)^3 - 7/324/(3*x + 2)^4