3.1135 \(\int \frac{(1-2 x) (3+5 x)}{2+3 x} \, dx\)

Optimal. Leaf size=23 \[ -\frac{5 x^2}{3}+\frac{17 x}{9}-\frac{7}{27} \log (3 x+2) \]

[Out]

(17*x)/9 - (5*x^2)/3 - (7*Log[2 + 3*x])/27

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Rubi [A]  time = 0.0271515, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{5 x^2}{3}+\frac{17 x}{9}-\frac{7}{27} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(17*x)/9 - (5*x^2)/3 - (7*Log[2 + 3*x])/27

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{7 \log{\left (3 x + 2 \right )}}{27} + \int \frac{17}{9}\, dx - \frac{10 \int x\, dx}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7*log(3*x + 2)/27 + Integral(17/9, x) - 10*Integral(x, x)/3

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Mathematica [A]  time = 0.00852083, size = 22, normalized size = 0.96 \[ \frac{1}{27} \left (-45 x^2+51 x-7 \log (3 x+2)+54\right ) \]

Antiderivative was successfully verified.

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

[Out]

(54 + 51*x - 45*x^2 - 7*Log[2 + 3*x])/27

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Maple [A]  time = 0.003, size = 18, normalized size = 0.8 \[{\frac{17\,x}{9}}-{\frac{5\,{x}^{2}}{3}}-{\frac{7\,\ln \left ( 2+3\,x \right ) }{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)/(2+3*x),x)

[Out]

17/9*x-5/3*x^2-7/27*ln(2+3*x)

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Maxima [A]  time = 1.37136, size = 23, normalized size = 1. \[ -\frac{5}{3} \, x^{2} + \frac{17}{9} \, x - \frac{7}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/3*x^2 + 17/9*x - 7/27*log(3*x + 2)

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Fricas [A]  time = 0.212368, size = 23, normalized size = 1. \[ -\frac{5}{3} \, x^{2} + \frac{17}{9} \, x - \frac{7}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/3*x^2 + 17/9*x - 7/27*log(3*x + 2)

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Sympy [A]  time = 0.135219, size = 20, normalized size = 0.87 \[ - \frac{5 x^{2}}{3} + \frac{17 x}{9} - \frac{7 \log{\left (3 x + 2 \right )}}{27} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5*x**2/3 + 17*x/9 - 7*log(3*x + 2)/27

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GIAC/XCAS [A]  time = 0.242385, size = 24, normalized size = 1.04 \[ -\frac{5}{3} \, x^{2} + \frac{17}{9} \, x - \frac{7}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/3*x^2 + 17/9*x - 7/27*ln(abs(3*x + 2))