3.1246 \(\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^2} \, dx\)

Optimal. Leaf size=41 \[ \frac{100 x^3}{27}-\frac{170 x^2}{27}+\frac{143 x}{27}-\frac{49}{243 (3 x+2)}-\frac{518}{243} \log (3 x+2) \]

[Out]

(143*x)/27 - (170*x^2)/27 + (100*x^3)/27 - 49/(243*(2 + 3*x)) - (518*Log[2 + 3*x
])/243

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Rubi [A]  time = 0.0546099, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{100 x^3}{27}-\frac{170 x^2}{27}+\frac{143 x}{27}-\frac{49}{243 (3 x+2)}-\frac{518}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(143*x)/27 - (170*x^2)/27 + (100*x^3)/27 - 49/(243*(2 + 3*x)) - (518*Log[2 + 3*x
])/243

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{100 x^{3}}{27} - \frac{518 \log{\left (3 x + 2 \right )}}{243} + \int \frac{143}{27}\, dx - \frac{340 \int x\, dx}{27} - \frac{49}{243 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

100*x**3/27 - 518*log(3*x + 2)/243 + Integral(143/27, x) - 340*Integral(x, x)/27
- 49/(243*(3*x + 2))

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Mathematica [A]  time = 0.0215717, size = 44, normalized size = 1.07 \[ \frac{8100 x^4-8370 x^3+2403 x^2+23964 x-1554 (3 x+2) \log (3 x+2)+10681}{729 (3 x+2)} \]

Antiderivative was successfully verified.

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

[Out]

(10681 + 23964*x + 2403*x^2 - 8370*x^3 + 8100*x^4 - 1554*(2 + 3*x)*Log[2 + 3*x])
/(729*(2 + 3*x))

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Maple [A]  time = 0.009, size = 32, normalized size = 0.8 \[{\frac{143\,x}{27}}-{\frac{170\,{x}^{2}}{27}}+{\frac{100\,{x}^{3}}{27}}-{\frac{49}{486+729\,x}}-{\frac{518\,\ln \left ( 2+3\,x \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

143/27*x-170/27*x^2+100/27*x^3-49/243/(2+3*x)-518/243*ln(2+3*x)

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Maxima [A]  time = 1.33766, size = 42, normalized size = 1.02 \[ \frac{100}{27} \, x^{3} - \frac{170}{27} \, x^{2} + \frac{143}{27} \, x - \frac{49}{243 \,{\left (3 \, x + 2\right )}} - \frac{518}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

100/27*x^3 - 170/27*x^2 + 143/27*x - 49/243/(3*x + 2) - 518/243*log(3*x + 2)

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Fricas [A]  time = 0.208307, size = 57, normalized size = 1.39 \[ \frac{2700 \, x^{4} - 2790 \, x^{3} + 801 \, x^{2} - 518 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 2574 \, x - 49}{243 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/243*(2700*x^4 - 2790*x^3 + 801*x^2 - 518*(3*x + 2)*log(3*x + 2) + 2574*x - 49)
/(3*x + 2)

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Sympy [A]  time = 0.224097, size = 34, normalized size = 0.83 \[ \frac{100 x^{3}}{27} - \frac{170 x^{2}}{27} + \frac{143 x}{27} - \frac{518 \log{\left (3 x + 2 \right )}}{243} - \frac{49}{729 x + 486} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

100*x**3/27 - 170*x**2/27 + 143*x/27 - 518*log(3*x + 2)/243 - 49/(729*x + 486)

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GIAC/XCAS [A]  time = 0.208574, size = 77, normalized size = 1.88 \[ -\frac{1}{729} \,{\left (3 \, x + 2\right )}^{3}{\left (\frac{1110}{3 \, x + 2} - \frac{4527}{{\left (3 \, x + 2\right )}^{2}} - 100\right )} - \frac{49}{243 \,{\left (3 \, x + 2\right )}} + \frac{518}{243} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/729*(3*x + 2)^3*(1110/(3*x + 2) - 4527/(3*x + 2)^2 - 100) - 49/243/(3*x + 2)
+ 518/243*ln(1/3*abs(3*x + 2)/(3*x + 2)^2)