3.1229 \(\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^2} \, dx\)

Optimal. Leaf size=34 \[ \frac{10 x^2}{9}-\frac{104 x}{27}+\frac{49}{81 (3 x+2)}+\frac{91}{27} \log (3 x+2) \]

[Out]

(-104*x)/27 + (10*x^2)/9 + 49/(81*(2 + 3*x)) + (91*Log[2 + 3*x])/27

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Rubi [A]  time = 0.0439829, antiderivative size = 34, 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 \[ \frac{10 x^2}{9}-\frac{104 x}{27}+\frac{49}{81 (3 x+2)}+\frac{91}{27} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(-104*x)/27 + (10*x^2)/9 + 49/(81*(2 + 3*x)) + (91*Log[2 + 3*x])/27

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{91 \log{\left (3 x + 2 \right )}}{27} + \int \left (- \frac{104}{27}\right )\, dx + \frac{20 \int x\, dx}{9} + \frac{49}{81 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

91*log(3*x + 2)/27 + Integral(-104/27, x) + 20*Integral(x, x)/9 + 49/(81*(3*x +
2))

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Mathematica [A]  time = 0.0187308, size = 39, normalized size = 1.15 \[ \frac{540 x^3-1512 x^2-447 x+546 (3 x+2) \log (6 x+4)+632}{162 (3 x+2)} \]

Antiderivative was successfully verified.

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

[Out]

(632 - 447*x - 1512*x^2 + 540*x^3 + 546*(2 + 3*x)*Log[4 + 6*x])/(162*(2 + 3*x))

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Maple [A]  time = 0.009, size = 27, normalized size = 0.8 \[ -{\frac{104\,x}{27}}+{\frac{10\,{x}^{2}}{9}}+{\frac{49}{162+243\,x}}+{\frac{91\,\ln \left ( 2+3\,x \right ) }{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-104/27*x+10/9*x^2+49/81/(2+3*x)+91/27*ln(2+3*x)

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Maxima [A]  time = 1.34506, size = 35, normalized size = 1.03 \[ \frac{10}{9} \, x^{2} - \frac{104}{27} \, x + \frac{49}{81 \,{\left (3 \, x + 2\right )}} + \frac{91}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10/9*x^2 - 104/27*x + 49/81/(3*x + 2) + 91/27*log(3*x + 2)

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Fricas [A]  time = 0.224534, size = 50, normalized size = 1.47 \[ \frac{270 \, x^{3} - 756 \, x^{2} + 273 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 624 \, x + 49}{81 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/81*(270*x^3 - 756*x^2 + 273*(3*x + 2)*log(3*x + 2) - 624*x + 49)/(3*x + 2)

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Sympy [A]  time = 0.20732, size = 27, normalized size = 0.79 \[ \frac{10 x^{2}}{9} - \frac{104 x}{27} + \frac{91 \log{\left (3 x + 2 \right )}}{27} + \frac{49}{243 x + 162} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10*x**2/9 - 104*x/27 + 91*log(3*x + 2)/27 + 49/(243*x + 162)

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GIAC/XCAS [A]  time = 0.211585, size = 65, normalized size = 1.91 \[ -\frac{2}{81} \,{\left (3 \, x + 2\right )}^{2}{\left (\frac{72}{3 \, x + 2} - 5\right )} + \frac{49}{81 \,{\left (3 \, x + 2\right )}} - \frac{91}{27} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/81*(3*x + 2)^2*(72/(3*x + 2) - 5) + 49/81/(3*x + 2) - 91/27*ln(1/3*abs(3*x +
2)/(3*x + 2)^2)