3.1247 \(\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^3} \, dx\)

Optimal. Leaf size=45 \[ \frac{50 x^2}{27}-\frac{20 x}{3}+\frac{518}{243 (3 x+2)}-\frac{49}{486 (3 x+2)^2}+\frac{503}{81} \log (3 x+2) \]

[Out]

(-20*x)/3 + (50*x^2)/27 - 49/(486*(2 + 3*x)^2) + 518/(243*(2 + 3*x)) + (503*Log[
2 + 3*x])/81

_______________________________________________________________________________________

Rubi [A]  time = 0.0592964, antiderivative size = 45, 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 \[ \frac{50 x^2}{27}-\frac{20 x}{3}+\frac{518}{243 (3 x+2)}-\frac{49}{486 (3 x+2)^2}+\frac{503}{81} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(-20*x)/3 + (50*x^2)/27 - 49/(486*(2 + 3*x)^2) + 518/(243*(2 + 3*x)) + (503*Log[
2 + 3*x])/81

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{503 \log{\left (3 x + 2 \right )}}{81} + \int \left (- \frac{20}{3}\right )\, dx + \frac{100 \int x\, dx}{27} + \frac{518}{243 \left (3 x + 2\right )} - \frac{49}{486 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

503*log(3*x + 2)/81 + Integral(-20/3, x) + 100*Integral(x, x)/27 + 518/(243*(3*x
+ 2)) - 49/(486*(3*x + 2)**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0288199, size = 42, normalized size = 0.93 \[ \frac{503}{81} \log (3 x+2)-\frac{-900 x^4+2040 x^3+6480 x^2+4508 x+913}{54 (3 x+2)^2} \]

Antiderivative was successfully verified.

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

[Out]

-(913 + 4508*x + 6480*x^2 + 2040*x^3 - 900*x^4)/(54*(2 + 3*x)^2) + (503*Log[2 +
3*x])/81

_______________________________________________________________________________________

Maple [A]  time = 0.01, size = 36, normalized size = 0.8 \[ -{\frac{20\,x}{3}}+{\frac{50\,{x}^{2}}{27}}-{\frac{49}{486\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{518}{486+729\,x}}+{\frac{503\,\ln \left ( 2+3\,x \right ) }{81}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20/3*x+50/27*x^2-49/486/(2+3*x)^2+518/243/(2+3*x)+503/81*ln(2+3*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34842, size = 49, normalized size = 1.09 \[ \frac{50}{27} \, x^{2} - \frac{20}{3} \, x + \frac{7 \,{\left (444 \, x + 289\right )}}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{503}{81} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50/27*x^2 - 20/3*x + 7/486*(444*x + 289)/(9*x^2 + 12*x + 4) + 503/81*log(3*x + 2
)

_______________________________________________________________________________________

Fricas [A]  time = 0.210664, size = 70, normalized size = 1.56 \[ \frac{8100 \, x^{4} - 18360 \, x^{3} - 35280 \, x^{2} + 3018 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 9852 \, x + 2023}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/486*(8100*x^4 - 18360*x^3 - 35280*x^2 + 3018*(9*x^2 + 12*x + 4)*log(3*x + 2) -
9852*x + 2023)/(9*x^2 + 12*x + 4)

_______________________________________________________________________________________

Sympy [A]  time = 0.269141, size = 36, normalized size = 0.8 \[ \frac{50 x^{2}}{27} - \frac{20 x}{3} + \frac{3108 x + 2023}{4374 x^{2} + 5832 x + 1944} + \frac{503 \log{\left (3 x + 2 \right )}}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50*x**2/27 - 20*x/3 + (3108*x + 2023)/(4374*x**2 + 5832*x + 1944) + 503*log(3*x
+ 2)/81

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.219235, size = 43, normalized size = 0.96 \[ \frac{50}{27} \, x^{2} - \frac{20}{3} \, x + \frac{7 \,{\left (444 \, x + 289\right )}}{486 \,{\left (3 \, x + 2\right )}^{2}} + \frac{503}{81} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

50/27*x^2 - 20/3*x + 7/486*(444*x + 289)/(3*x + 2)^2 + 503/81*ln(abs(3*x + 2))