3.1181 \(\int \frac{(1-2 x) (2+3 x)}{3+5 x} \, dx\)

Optimal. Leaf size=23 \[ -\frac{3 x^2}{5}+\frac{13 x}{25}+\frac{11}{125} \log (5 x+3) \]

[Out]

(13*x)/25 - (3*x^2)/5 + (11*Log[3 + 5*x])/125

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Rubi [A]  time = 0.0256482, 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 \[ -\frac{3 x^2}{5}+\frac{13 x}{25}+\frac{11}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(13*x)/25 - (3*x^2)/5 + (11*Log[3 + 5*x])/125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{11 \log{\left (5 x + 3 \right )}}{125} + \int \frac{13}{25}\, dx - \frac{6 \int x\, dx}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

11*log(5*x + 3)/125 + Integral(13/25, x) - 6*Integral(x, x)/5

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Mathematica [A]  time = 0.00815381, size = 22, normalized size = 0.96 \[ \frac{1}{125} \left (-75 x^2+65 x+11 \log (5 x+3)+66\right ) \]

Antiderivative was successfully verified.

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

[Out]

(66 + 65*x - 75*x^2 + 11*Log[3 + 5*x])/125

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Maple [A]  time = 0.003, size = 18, normalized size = 0.8 \[{\frac{13\,x}{25}}-{\frac{3\,{x}^{2}}{5}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)/(3+5*x),x)

[Out]

13/25*x-3/5*x^2+11/125*ln(3+5*x)

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Maxima [A]  time = 1.35025, size = 23, normalized size = 1. \[ -\frac{3}{5} \, x^{2} + \frac{13}{25} \, x + \frac{11}{125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3/5*x^2 + 13/25*x + 11/125*log(5*x + 3)

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Fricas [A]  time = 0.206377, size = 23, normalized size = 1. \[ -\frac{3}{5} \, x^{2} + \frac{13}{25} \, x + \frac{11}{125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3/5*x^2 + 13/25*x + 11/125*log(5*x + 3)

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Sympy [A]  time = 0.139884, size = 20, normalized size = 0.87 \[ - \frac{3 x^{2}}{5} + \frac{13 x}{25} + \frac{11 \log{\left (5 x + 3 \right )}}{125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3*x**2/5 + 13*x/25 + 11*log(5*x + 3)/125

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GIAC/XCAS [A]  time = 0.211257, size = 24, normalized size = 1.04 \[ -\frac{3}{5} \, x^{2} + \frac{13}{25} \, x + \frac{11}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3/5*x^2 + 13/25*x + 11/125*ln(abs(5*x + 3))