3.1294 \(\int \frac{(1-2 x)^2 (2+3 x)}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=34 \[ \frac{6 x^2}{25}-\frac{92 x}{125}-\frac{121}{625 (5 x+3)}+\frac{319}{625} \log (5 x+3) \]

[Out]

(-92*x)/125 + (6*x^2)/25 - 121/(625*(3 + 5*x)) + (319*Log[3 + 5*x])/625

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Rubi [A]  time = 0.0434111, antiderivative size = 34, 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 \[ \frac{6 x^2}{25}-\frac{92 x}{125}-\frac{121}{625 (5 x+3)}+\frac{319}{625} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(-92*x)/125 + (6*x^2)/25 - 121/(625*(3 + 5*x)) + (319*Log[3 + 5*x])/625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{319 \log{\left (5 x + 3 \right )}}{625} + \int \left (- \frac{92}{125}\right )\, dx + \frac{12 \int x\, dx}{25} - \frac{121}{625 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

319*log(5*x + 3)/625 + Integral(-92/125, x) + 12*Integral(x, x)/25 - 121/(625*(5
*x + 3))

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Mathematica [A]  time = 0.0194799, size = 39, normalized size = 1.15 \[ \frac{1500 x^3-3700 x^2-835 x+638 (5 x+3) \log (10 x+6)+913}{1250 (5 x+3)} \]

Antiderivative was successfully verified.

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

[Out]

(913 - 835*x - 3700*x^2 + 1500*x^3 + 638*(3 + 5*x)*Log[6 + 10*x])/(1250*(3 + 5*x
))

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Maple [A]  time = 0.008, size = 27, normalized size = 0.8 \[ -{\frac{92\,x}{125}}+{\frac{6\,{x}^{2}}{25}}-{\frac{121}{1875+3125\,x}}+{\frac{319\,\ln \left ( 3+5\,x \right ) }{625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-92/125*x+6/25*x^2-121/625/(3+5*x)+319/625*ln(3+5*x)

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Maxima [A]  time = 1.34636, size = 35, normalized size = 1.03 \[ \frac{6}{25} \, x^{2} - \frac{92}{125} \, x - \frac{121}{625 \,{\left (5 \, x + 3\right )}} + \frac{319}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

6/25*x^2 - 92/125*x - 121/625/(5*x + 3) + 319/625*log(5*x + 3)

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Fricas [A]  time = 0.212755, size = 50, normalized size = 1.47 \[ \frac{750 \, x^{3} - 1850 \, x^{2} + 319 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1380 \, x - 121}{625 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/625*(750*x^3 - 1850*x^2 + 319*(5*x + 3)*log(5*x + 3) - 1380*x - 121)/(5*x + 3)

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Sympy [A]  time = 0.207373, size = 27, normalized size = 0.79 \[ \frac{6 x^{2}}{25} - \frac{92 x}{125} + \frac{319 \log{\left (5 x + 3 \right )}}{625} - \frac{121}{3125 x + 1875} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

6*x**2/25 - 92*x/125 + 319*log(5*x + 3)/625 - 121/(3125*x + 1875)

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GIAC/XCAS [A]  time = 0.211116, size = 65, normalized size = 1.91 \[ -\frac{2}{625} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{64}{5 \, x + 3} - 3\right )} - \frac{121}{625 \,{\left (5 \, x + 3\right )}} - \frac{319}{625} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/625*(5*x + 3)^2*(64/(5*x + 3) - 3) - 121/625/(5*x + 3) - 319/625*ln(1/5*abs(5
*x + 3)/(5*x + 3)^2)