3.1264 \(\int \frac{(1-2 x)^2 (3+5 x)^3}{2+3 x} \, dx\)

Optimal. Leaf size=44 \[ \frac{100 x^5}{3}+\frac{50 x^4}{9}-\frac{2515 x^3}{81}-\frac{559 x^2}{162}+\frac{3305 x}{243}-\frac{49}{729} \log (3 x+2) \]

[Out]

(3305*x)/243 - (559*x^2)/162 - (2515*x^3)/81 + (50*x^4)/9 + (100*x^5)/3 - (49*Lo
g[2 + 3*x])/729

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Rubi [A]  time = 0.048391, antiderivative size = 44, 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 \[ \frac{100 x^5}{3}+\frac{50 x^4}{9}-\frac{2515 x^3}{81}-\frac{559 x^2}{162}+\frac{3305 x}{243}-\frac{49}{729} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(3305*x)/243 - (559*x^2)/162 - (2515*x^3)/81 + (50*x^4)/9 + (100*x^5)/3 - (49*Lo
g[2 + 3*x])/729

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{100 x^{5}}{3} + \frac{50 x^{4}}{9} - \frac{2515 x^{3}}{81} - \frac{49 \log{\left (3 x + 2 \right )}}{729} + \int \frac{3305}{243}\, dx - \frac{559 \int x\, dx}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

100*x**5/3 + 50*x**4/9 - 2515*x**3/81 - 49*log(3*x + 2)/729 + Integral(3305/243,
x) - 559*Integral(x, x)/81

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Mathematica [A]  time = 0.0179187, size = 37, normalized size = 0.84 \[ \frac{145800 x^5+24300 x^4-135810 x^3-15093 x^2+59490 x-294 \log (3 x+2)+20528}{4374} \]

Antiderivative was successfully verified.

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

[Out]

(20528 + 59490*x - 15093*x^2 - 135810*x^3 + 24300*x^4 + 145800*x^5 - 294*Log[2 +
3*x])/4374

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Maple [A]  time = 0.004, size = 33, normalized size = 0.8 \[{\frac{3305\,x}{243}}-{\frac{559\,{x}^{2}}{162}}-{\frac{2515\,{x}^{3}}{81}}+{\frac{50\,{x}^{4}}{9}}+{\frac{100\,{x}^{5}}{3}}-{\frac{49\,\ln \left ( 2+3\,x \right ) }{729}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3305/243*x-559/162*x^2-2515/81*x^3+50/9*x^4+100/3*x^5-49/729*ln(2+3*x)

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Maxima [A]  time = 1.33425, size = 43, normalized size = 0.98 \[ \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

100/3*x^5 + 50/9*x^4 - 2515/81*x^3 - 559/162*x^2 + 3305/243*x - 49/729*log(3*x +
2)

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Fricas [A]  time = 0.207935, size = 43, normalized size = 0.98 \[ \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

100/3*x^5 + 50/9*x^4 - 2515/81*x^3 - 559/162*x^2 + 3305/243*x - 49/729*log(3*x +
2)

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Sympy [A]  time = 0.176873, size = 41, normalized size = 0.93 \[ \frac{100 x^{5}}{3} + \frac{50 x^{4}}{9} - \frac{2515 x^{3}}{81} - \frac{559 x^{2}}{162} + \frac{3305 x}{243} - \frac{49 \log{\left (3 x + 2 \right )}}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

100*x**5/3 + 50*x**4/9 - 2515*x**3/81 - 559*x**2/162 + 3305*x/243 - 49*log(3*x +
2)/729

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GIAC/XCAS [A]  time = 0.222979, size = 45, normalized size = 1.02 \[ \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

100/3*x^5 + 50/9*x^4 - 2515/81*x^3 - 559/162*x^2 + 3305/243*x - 49/729*ln(abs(3*
x + 2))