3.1151 \(\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^2} \, dx\)

Optimal. Leaf size=34 \[ -\frac{25 x^2}{9}+\frac{95 x}{27}-\frac{7}{81 (3 x+2)}-\frac{8}{9} \log (3 x+2) \]

[Out]

(95*x)/27 - (25*x^2)/9 - 7/(81*(2 + 3*x)) - (8*Log[2 + 3*x])/9

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Rubi [A]  time = 0.0453784, 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 \[ -\frac{25 x^2}{9}+\frac{95 x}{27}-\frac{7}{81 (3 x+2)}-\frac{8}{9} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(95*x)/27 - (25*x^2)/9 - 7/(81*(2 + 3*x)) - (8*Log[2 + 3*x])/9

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{8 \log{\left (3 x + 2 \right )}}{9} + \int \frac{95}{27}\, dx - \frac{50 \int x\, dx}{9} - \frac{7}{81 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*log(3*x + 2)/9 + Integral(95/27, x) - 50*Integral(x, x)/9 - 7/(81*(3*x + 2))

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Mathematica [A]  time = 0.0167949, size = 36, normalized size = 1.06 \[ \frac{-225 x^3+135 x^2+480 x-24 (3 x+2) \log (3 x+2)+191}{81 x+54} \]

Antiderivative was successfully verified.

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

[Out]

(191 + 480*x + 135*x^2 - 225*x^3 - 24*(2 + 3*x)*Log[2 + 3*x])/(54 + 81*x)

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Maple [A]  time = 0.009, size = 27, normalized size = 0.8 \[{\frac{95\,x}{27}}-{\frac{25\,{x}^{2}}{9}}-{\frac{7}{162+243\,x}}-{\frac{8\,\ln \left ( 2+3\,x \right ) }{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

95/27*x-25/9*x^2-7/81/(2+3*x)-8/9*ln(2+3*x)

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Maxima [A]  time = 1.34565, size = 35, normalized size = 1.03 \[ -\frac{25}{9} \, x^{2} + \frac{95}{27} \, x - \frac{7}{81 \,{\left (3 \, x + 2\right )}} - \frac{8}{9} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/9*x^2 + 95/27*x - 7/81/(3*x + 2) - 8/9*log(3*x + 2)

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Fricas [A]  time = 0.22001, size = 50, normalized size = 1.47 \[ -\frac{675 \, x^{3} - 405 \, x^{2} + 72 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 570 \, x + 7}{81 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/81*(675*x^3 - 405*x^2 + 72*(3*x + 2)*log(3*x + 2) - 570*x + 7)/(3*x + 2)

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Sympy [A]  time = 0.21019, size = 27, normalized size = 0.79 \[ - \frac{25 x^{2}}{9} + \frac{95 x}{27} - \frac{8 \log{\left (3 x + 2 \right )}}{9} - \frac{7}{243 x + 162} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*x**2/9 + 95*x/27 - 8*log(3*x + 2)/9 - 7/(243*x + 162)

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GIAC/XCAS [A]  time = 0.218489, size = 65, normalized size = 1.91 \[ \frac{5}{81} \,{\left (3 \, x + 2\right )}^{2}{\left (\frac{39}{3 \, x + 2} - 5\right )} - \frac{7}{81 \,{\left (3 \, x + 2\right )}} + \frac{8}{9} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/81*(3*x + 2)^2*(39/(3*x + 2) - 5) - 7/81/(3*x + 2) + 8/9*ln(1/3*abs(3*x + 2)/(
3*x + 2)^2)