3.1139 \(\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^5} \, dx\)

Optimal. Leaf size=34 \[ \frac{5}{27 (3 x+2)^2}-\frac{37}{81 (3 x+2)^3}+\frac{7}{108 (3 x+2)^4} \]

[Out]

7/(108*(2 + 3*x)^4) - 37/(81*(2 + 3*x)^3) + 5/(27*(2 + 3*x)^2)

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Rubi [A]  time = 0.0376457, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{5}{27 (3 x+2)^2}-\frac{37}{81 (3 x+2)^3}+\frac{7}{108 (3 x+2)^4} \]

Antiderivative was successfully verified.

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

[Out]

7/(108*(2 + 3*x)^4) - 37/(81*(2 + 3*x)^3) + 5/(27*(2 + 3*x)^2)

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Rubi in Sympy [A]  time = 6.44165, size = 29, normalized size = 0.85 \[ \frac{5}{27 \left (3 x + 2\right )^{2}} - \frac{37}{81 \left (3 x + 2\right )^{3}} + \frac{7}{108 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/(27*(3*x + 2)**2) - 37/(81*(3*x + 2)**3) + 7/(108*(3*x + 2)**4)

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Mathematica [A]  time = 0.00852275, size = 21, normalized size = 0.62 \[ \frac{540 x^2+276 x-35}{324 (3 x+2)^4} \]

Antiderivative was successfully verified.

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

[Out]

(-35 + 276*x + 540*x^2)/(324*(2 + 3*x)^4)

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Maple [A]  time = 0.007, size = 29, normalized size = 0.9 \[{\frac{7}{108\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{37}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{5}{27\, \left ( 2+3\,x \right ) ^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7/108/(2+3*x)^4-37/81/(2+3*x)^3+5/27/(2+3*x)^2

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Maxima [A]  time = 1.35063, size = 46, normalized size = 1.35 \[ \frac{540 \, x^{2} + 276 \, x - 35}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/324*(540*x^2 + 276*x - 35)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Fricas [A]  time = 0.201709, size = 46, normalized size = 1.35 \[ \frac{540 \, x^{2} + 276 \, x - 35}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/324*(540*x^2 + 276*x - 35)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Sympy [A]  time = 0.301087, size = 29, normalized size = 0.85 \[ \frac{540 x^{2} + 276 x - 35}{26244 x^{4} + 69984 x^{3} + 69984 x^{2} + 31104 x + 5184} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(540*x**2 + 276*x - 35)/(26244*x**4 + 69984*x**3 + 69984*x**2 + 31104*x + 5184)

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GIAC/XCAS [A]  time = 0.21031, size = 38, normalized size = 1.12 \[ \frac{5}{27 \,{\left (3 \, x + 2\right )}^{2}} - \frac{37}{81 \,{\left (3 \, x + 2\right )}^{3}} + \frac{7}{108 \,{\left (3 \, x + 2\right )}^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/27/(3*x + 2)^2 - 37/81/(3*x + 2)^3 + 7/108/(3*x + 2)^4