3.1350 \(\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^4} \, dx\)

Optimal. Leaf size=56 \[ -\frac{100 x^2}{81}+\frac{1780 x}{243}-\frac{11599}{729 (3 x+2)}+\frac{1862}{729 (3 x+2)^2}-\frac{343}{2187 (3 x+2)^3}-\frac{8198}{729} \log (3 x+2) \]

[Out]

(1780*x)/243 - (100*x^2)/81 - 343/(2187*(2 + 3*x)^3) + 1862/(729*(2 + 3*x)^2) -
11599/(729*(2 + 3*x)) - (8198*Log[2 + 3*x])/729

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Rubi [A]  time = 0.0690735, antiderivative size = 56, 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 \[ -\frac{100 x^2}{81}+\frac{1780 x}{243}-\frac{11599}{729 (3 x+2)}+\frac{1862}{729 (3 x+2)^2}-\frac{343}{2187 (3 x+2)^3}-\frac{8198}{729} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(1780*x)/243 - (100*x^2)/81 - 343/(2187*(2 + 3*x)^3) + 1862/(729*(2 + 3*x)^2) -
11599/(729*(2 + 3*x)) - (8198*Log[2 + 3*x])/729

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{8198 \log{\left (3 x + 2 \right )}}{729} + \int \frac{1780}{243}\, dx - \frac{200 \int x\, dx}{81} - \frac{11599}{729 \left (3 x + 2\right )} + \frac{1862}{729 \left (3 x + 2\right )^{2}} - \frac{343}{2187 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8198*log(3*x + 2)/729 + Integral(1780/243, x) - 200*Integral(x, x)/81 - 11599/(
729*(3*x + 2)) + 1862/(729*(3*x + 2)**2) - 343/(2187*(3*x + 2)**3)

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Mathematica [A]  time = 0.0503391, size = 51, normalized size = 0.91 \[ \frac{-72900 x^5+286740 x^4+1088640 x^3+883467 x^2+155034 x-24594 (3 x+2)^3 \log (30 x+20)-33319}{2187 (3 x+2)^3} \]

Antiderivative was successfully verified.

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

[Out]

(-33319 + 155034*x + 883467*x^2 + 1088640*x^3 + 286740*x^4 - 72900*x^5 - 24594*(
2 + 3*x)^3*Log[20 + 30*x])/(2187*(2 + 3*x)^3)

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Maple [A]  time = 0.01, size = 45, normalized size = 0.8 \[{\frac{1780\,x}{243}}-{\frac{100\,{x}^{2}}{81}}-{\frac{343}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1862}{729\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{11599}{1458+2187\,x}}-{\frac{8198\,\ln \left ( 2+3\,x \right ) }{729}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1780/243*x-100/81*x^2-343/2187/(2+3*x)^3+1862/729/(2+3*x)^2-11599/729/(2+3*x)-81
98/729*ln(2+3*x)

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Maxima [A]  time = 1.33521, size = 62, normalized size = 1.11 \[ -\frac{100}{81} \, x^{2} + \frac{1780}{243} \, x - \frac{7 \,{\left (44739 \, x^{2} + 57258 \, x + 18337\right )}}{2187 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac{8198}{729} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-100/81*x^2 + 1780/243*x - 7/2187*(44739*x^2 + 57258*x + 18337)/(27*x^3 + 54*x^2
+ 36*x + 8) - 8198/729*log(3*x + 2)

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Fricas [A]  time = 0.213804, size = 90, normalized size = 1.61 \[ -\frac{72900 \, x^{5} - 286740 \, x^{4} - 767880 \, x^{3} - 241947 \, x^{2} + 24594 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 272646 \, x + 128359}{2187 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2187*(72900*x^5 - 286740*x^4 - 767880*x^3 - 241947*x^2 + 24594*(27*x^3 + 54*x
^2 + 36*x + 8)*log(3*x + 2) + 272646*x + 128359)/(27*x^3 + 54*x^2 + 36*x + 8)

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Sympy [A]  time = 0.345904, size = 46, normalized size = 0.82 \[ - \frac{100 x^{2}}{81} + \frac{1780 x}{243} - \frac{313173 x^{2} + 400806 x + 128359}{59049 x^{3} + 118098 x^{2} + 78732 x + 17496} - \frac{8198 \log{\left (3 x + 2 \right )}}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-100*x**2/81 + 1780*x/243 - (313173*x**2 + 400806*x + 128359)/(59049*x**3 + 1180
98*x**2 + 78732*x + 17496) - 8198*log(3*x + 2)/729

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GIAC/XCAS [A]  time = 0.212167, size = 50, normalized size = 0.89 \[ -\frac{100}{81} \, x^{2} + \frac{1780}{243} \, x - \frac{7 \,{\left (44739 \, x^{2} + 57258 \, x + 18337\right )}}{2187 \,{\left (3 \, x + 2\right )}^{3}} - \frac{8198}{729} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-100/81*x^2 + 1780/243*x - 7/2187*(44739*x^2 + 57258*x + 18337)/(3*x + 2)^3 - 81
98/729*ln(abs(3*x + 2))