3.1153 \(\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^4} \, dx\)

Optimal. Leaf size=44 \[ -\frac{65}{27 (3 x+2)}+\frac{4}{9 (3 x+2)^2}-\frac{7}{243 (3 x+2)^3}-\frac{50}{81} \log (3 x+2) \]

[Out]

-7/(243*(2 + 3*x)^3) + 4/(9*(2 + 3*x)^2) - 65/(27*(2 + 3*x)) - (50*Log[2 + 3*x])
/81

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Rubi [A]  time = 0.0463851, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{65}{27 (3 x+2)}+\frac{4}{9 (3 x+2)^2}-\frac{7}{243 (3 x+2)^3}-\frac{50}{81} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^4,x]

[Out]

-7/(243*(2 + 3*x)^3) + 4/(9*(2 + 3*x)^2) - 65/(27*(2 + 3*x)) - (50*Log[2 + 3*x])
/81

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Rubi in Sympy [A]  time = 7.69859, size = 36, normalized size = 0.82 \[ - \frac{50 \log{\left (3 x + 2 \right )}}{81} - \frac{65}{27 \left (3 x + 2\right )} + \frac{4}{9 \left (3 x + 2\right )^{2}} - \frac{7}{243 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(3+5*x)**2/(2+3*x)**4,x)

[Out]

-50*log(3*x + 2)/81 - 65/(27*(3*x + 2)) + 4/(9*(3*x + 2)**2) - 7/(243*(3*x + 2)*
*3)

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Mathematica [A]  time = 0.0229441, size = 36, normalized size = 0.82 \[ -\frac{5265 x^2+6696 x+150 (3 x+2)^3 \log (3 x+2)+2131}{243 (3 x+2)^3} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^4,x]

[Out]

-(2131 + 6696*x + 5265*x^2 + 150*(2 + 3*x)^3*Log[2 + 3*x])/(243*(2 + 3*x)^3)

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Maple [A]  time = 0.009, size = 37, normalized size = 0.8 \[ -{\frac{7}{243\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{4}{9\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{65}{54+81\,x}}-{\frac{50\,\ln \left ( 2+3\,x \right ) }{81}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)^2/(2+3*x)^4,x)

[Out]

-7/243/(2+3*x)^3+4/9/(2+3*x)^2-65/27/(2+3*x)-50/81*ln(2+3*x)

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Maxima [A]  time = 1.34705, size = 51, normalized size = 1.16 \[ -\frac{5265 \, x^{2} + 6696 \, x + 2131}{243 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac{50}{81} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^4,x, algorithm="maxima")

[Out]

-1/243*(5265*x^2 + 6696*x + 2131)/(27*x^3 + 54*x^2 + 36*x + 8) - 50/81*log(3*x +
2)

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Fricas [A]  time = 0.214283, size = 70, normalized size = 1.59 \[ -\frac{5265 \, x^{2} + 150 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 6696 \, x + 2131}{243 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^4,x, algorithm="fricas")

[Out]

-1/243*(5265*x^2 + 150*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 6696*x + 2131
)/(27*x^3 + 54*x^2 + 36*x + 8)

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Sympy [A]  time = 0.319789, size = 36, normalized size = 0.82 \[ - \frac{5265 x^{2} + 6696 x + 2131}{6561 x^{3} + 13122 x^{2} + 8748 x + 1944} - \frac{50 \log{\left (3 x + 2 \right )}}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x)**2/(2+3*x)**4,x)

[Out]

-(5265*x**2 + 6696*x + 2131)/(6561*x**3 + 13122*x**2 + 8748*x + 1944) - 50*log(3
*x + 2)/81

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GIAC/XCAS [A]  time = 0.209858, size = 39, normalized size = 0.89 \[ -\frac{5265 \, x^{2} + 6696 \, x + 2131}{243 \,{\left (3 \, x + 2\right )}^{3}} - \frac{50}{81} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)/(3*x + 2)^4,x, algorithm="giac")

[Out]

-1/243*(5265*x^2 + 6696*x + 2131)/(3*x + 2)^3 - 50/81*ln(abs(3*x + 2))