3.1150 \(\int \frac{(1-2 x) (3+5 x)^2}{2+3 x} \, dx\)

Optimal. Leaf size=30 \[ -\frac{50 x^3}{9}-\frac{5 x^2}{18}+\frac{118 x}{27}+\frac{7}{81} \log (3 x+2) \]

[Out]

(118*x)/27 - (5*x^2)/18 - (50*x^3)/9 + (7*Log[2 + 3*x])/81

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Rubi [A]  time = 0.0338296, antiderivative size = 30, 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 \[ -\frac{50 x^3}{9}-\frac{5 x^2}{18}+\frac{118 x}{27}+\frac{7}{81} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(118*x)/27 - (5*x^2)/18 - (50*x^3)/9 + (7*Log[2 + 3*x])/81

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{50 x^{3}}{9} + \frac{7 \log{\left (3 x + 2 \right )}}{81} + \int \frac{118}{27}\, dx - \frac{5 \int x\, dx}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50*x**3/9 + 7*log(3*x + 2)/81 + Integral(118/27, x) - 5*Integral(x, x)/9

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Mathematica [A]  time = 0.0151938, size = 27, normalized size = 0.9 \[ \frac{1}{486} \left (-2700 x^3-135 x^2+2124 x+42 \log (3 x+2)+676\right ) \]

Antiderivative was successfully verified.

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

[Out]

(676 + 2124*x - 135*x^2 - 2700*x^3 + 42*Log[2 + 3*x])/486

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Maple [A]  time = 0.004, size = 23, normalized size = 0.8 \[{\frac{118\,x}{27}}-{\frac{5\,{x}^{2}}{18}}-{\frac{50\,{x}^{3}}{9}}+{\frac{7\,\ln \left ( 2+3\,x \right ) }{81}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

118/27*x-5/18*x^2-50/9*x^3+7/81*ln(2+3*x)

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Maxima [A]  time = 1.34627, size = 30, normalized size = 1. \[ -\frac{50}{9} \, x^{3} - \frac{5}{18} \, x^{2} + \frac{118}{27} \, x + \frac{7}{81} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50/9*x^3 - 5/18*x^2 + 118/27*x + 7/81*log(3*x + 2)

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Fricas [A]  time = 0.20923, size = 30, normalized size = 1. \[ -\frac{50}{9} \, x^{3} - \frac{5}{18} \, x^{2} + \frac{118}{27} \, x + \frac{7}{81} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50/9*x^3 - 5/18*x^2 + 118/27*x + 7/81*log(3*x + 2)

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Sympy [A]  time = 0.170057, size = 27, normalized size = 0.9 \[ - \frac{50 x^{3}}{9} - \frac{5 x^{2}}{18} + \frac{118 x}{27} + \frac{7 \log{\left (3 x + 2 \right )}}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50*x**3/9 - 5*x**2/18 + 118*x/27 + 7*log(3*x + 2)/81

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GIAC/XCAS [A]  time = 0.209964, size = 31, normalized size = 1.03 \[ -\frac{50}{9} \, x^{3} - \frac{5}{18} \, x^{2} + \frac{118}{27} \, x + \frac{7}{81} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-50/9*x^3 - 5/18*x^2 + 118/27*x + 7/81*ln(abs(3*x + 2))