3.1140 \(\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^6} \, dx\)

Optimal. Leaf size=34 \[ \frac{10}{81 (3 x+2)^3}-\frac{37}{108 (3 x+2)^4}+\frac{7}{135 (3 x+2)^5} \]

[Out]

7/(135*(2 + 3*x)^5) - 37/(108*(2 + 3*x)^4) + 10/(81*(2 + 3*x)^3)

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Rubi [A]  time = 0.037511, 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 \[ \frac{10}{81 (3 x+2)^3}-\frac{37}{108 (3 x+2)^4}+\frac{7}{135 (3 x+2)^5} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^6,x]

[Out]

7/(135*(2 + 3*x)^5) - 37/(108*(2 + 3*x)^4) + 10/(81*(2 + 3*x)^3)

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Rubi in Sympy [A]  time = 6.49375, size = 29, normalized size = 0.85 \[ \frac{10}{81 \left (3 x + 2\right )^{3}} - \frac{37}{108 \left (3 x + 2\right )^{4}} + \frac{7}{135 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(3+5*x)/(2+3*x)**6,x)

[Out]

10/(81*(3*x + 2)**3) - 37/(108*(3*x + 2)**4) + 7/(135*(3*x + 2)**5)

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Mathematica [A]  time = 0.00985068, size = 21, normalized size = 0.62 \[ \frac{1800 x^2+735 x-226}{1620 (3 x+2)^5} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^6,x]

[Out]

(-226 + 735*x + 1800*x^2)/(1620*(2 + 3*x)^5)

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Maple [A]  time = 0.007, size = 29, normalized size = 0.9 \[{\frac{7}{135\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{37}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{10}{81\, \left ( 2+3\,x \right ) ^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)/(2+3*x)^6,x)

[Out]

7/135/(2+3*x)^5-37/108/(2+3*x)^4+10/81/(2+3*x)^3

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Maxima [A]  time = 1.33311, size = 53, normalized size = 1.56 \[ \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)/(3*x + 2)^6,x, algorithm="maxima")

[Out]

1/1620*(1800*x^2 + 735*x - 226)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x
+ 32)

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Fricas [A]  time = 0.206423, size = 53, normalized size = 1.56 \[ \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)/(3*x + 2)^6,x, algorithm="fricas")

[Out]

1/1620*(1800*x^2 + 735*x - 226)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x
+ 32)

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Sympy [A]  time = 0.342035, size = 34, normalized size = 1. \[ \frac{1800 x^{2} + 735 x - 226}{393660 x^{5} + 1312200 x^{4} + 1749600 x^{3} + 1166400 x^{2} + 388800 x + 51840} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x)/(2+3*x)**6,x)

[Out]

(1800*x**2 + 735*x - 226)/(393660*x**5 + 1312200*x**4 + 1749600*x**3 + 1166400*x
**2 + 388800*x + 51840)

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GIAC/XCAS [A]  time = 0.212411, size = 26, normalized size = 0.76 \[ \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (3 \, x + 2\right )}^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)/(3*x + 2)^6,x, algorithm="giac")

[Out]

1/1620*(1800*x^2 + 735*x - 226)/(3*x + 2)^5