3.1137 \(\int \frac{(1-2 x) (3+5 x)}{(2+3 x)^3} \, dx\)

Optimal. Leaf size=33 \[ -\frac{37}{27 (3 x+2)}+\frac{7}{54 (3 x+2)^2}-\frac{10}{27} \log (3 x+2) \]

[Out]

7/(54*(2 + 3*x)^2) - 37/(27*(2 + 3*x)) - (10*Log[2 + 3*x])/27

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Rubi [A]  time = 0.035082, antiderivative size = 33, 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 \[ -\frac{37}{27 (3 x+2)}+\frac{7}{54 (3 x+2)^2}-\frac{10}{27} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

7/(54*(2 + 3*x)^2) - 37/(27*(2 + 3*x)) - (10*Log[2 + 3*x])/27

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Rubi in Sympy [A]  time = 6.14524, size = 26, normalized size = 0.79 \[ - \frac{10 \log{\left (3 x + 2 \right )}}{27} - \frac{37}{27 \left (3 x + 2\right )} + \frac{7}{54 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-10*log(3*x + 2)/27 - 37/(27*(3*x + 2)) + 7/(54*(3*x + 2)**2)

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Mathematica [A]  time = 0.0154645, size = 27, normalized size = 0.82 \[ \frac{1}{54} \left (-\frac{3 (74 x+47)}{(3 x+2)^2}-20 \log (3 x+2)\right ) \]

Antiderivative was successfully verified.

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

[Out]

((-3*(47 + 74*x))/(2 + 3*x)^2 - 20*Log[2 + 3*x])/54

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Maple [A]  time = 0.01, size = 28, normalized size = 0.9 \[{\frac{7}{54\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{37}{54+81\,x}}-{\frac{10\,\ln \left ( 2+3\,x \right ) }{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7/54/(2+3*x)^2-37/27/(2+3*x)-10/27*ln(2+3*x)

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Maxima [A]  time = 1.34524, size = 38, normalized size = 1.15 \[ -\frac{74 \, x + 47}{18 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{10}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/18*(74*x + 47)/(9*x^2 + 12*x + 4) - 10/27*log(3*x + 2)

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Fricas [A]  time = 0.218053, size = 50, normalized size = 1.52 \[ -\frac{20 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 222 \, x + 141}{54 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/54*(20*(9*x^2 + 12*x + 4)*log(3*x + 2) + 222*x + 141)/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.236063, size = 26, normalized size = 0.79 \[ - \frac{74 x + 47}{162 x^{2} + 216 x + 72} - \frac{10 \log{\left (3 x + 2 \right )}}{27} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(74*x + 47)/(162*x**2 + 216*x + 72) - 10*log(3*x + 2)/27

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GIAC/XCAS [A]  time = 0.233777, size = 32, normalized size = 0.97 \[ -\frac{74 \, x + 47}{18 \,{\left (3 \, x + 2\right )}^{2}} - \frac{10}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/18*(74*x + 47)/(3*x + 2)^2 - 10/27*ln(abs(3*x + 2))