3.1378 \(\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)} \, dx\)

Optimal. Leaf size=33 \[ -\frac{4 x^2}{15}+\frac{332 x}{225}-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3) \]

[Out]

(332*x)/225 - (4*x^2)/15 - (343*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/125

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Rubi [A]  time = 0.0429702, antiderivative size = 33, 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 \[ -\frac{4 x^2}{15}+\frac{332 x}{225}-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(332*x)/225 - (4*x^2)/15 - (343*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{343 \log{\left (3 x + 2 \right )}}{27} + \frac{1331 \log{\left (5 x + 3 \right )}}{125} + \int \frac{332}{225}\, dx - \frac{8 \int x\, dx}{15} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-343*log(3*x + 2)/27 + 1331*log(5*x + 3)/125 + Integral(332/225, x) - 8*Integral
(x, x)/15

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Mathematica [A]  time = 0.0220859, size = 35, normalized size = 1.06 \[ \frac{60 \left (-15 x^2+83 x+62\right )-42875 \log (3 x+2)+35937 \log (-3 (5 x+3))}{3375} \]

Antiderivative was successfully verified.

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

[Out]

(60*(62 + 83*x - 15*x^2) - 42875*Log[2 + 3*x] + 35937*Log[-3*(3 + 5*x)])/3375

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Maple [A]  time = 0.008, size = 26, normalized size = 0.8 \[{\frac{332\,x}{225}}-{\frac{4\,{x}^{2}}{15}}-{\frac{343\,\ln \left ( 2+3\,x \right ) }{27}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

332/225*x-4/15*x^2-343/27*ln(2+3*x)+1331/125*ln(3+5*x)

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Maxima [A]  time = 1.34454, size = 34, normalized size = 1.03 \[ -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log \left (5 \, x + 3\right ) - \frac{343}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-4/15*x^2 + 332/225*x + 1331/125*log(5*x + 3) - 343/27*log(3*x + 2)

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Fricas [A]  time = 0.208974, size = 34, normalized size = 1.03 \[ -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log \left (5 \, x + 3\right ) - \frac{343}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-4/15*x^2 + 332/225*x + 1331/125*log(5*x + 3) - 343/27*log(3*x + 2)

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Sympy [A]  time = 0.269938, size = 31, normalized size = 0.94 \[ - \frac{4 x^{2}}{15} + \frac{332 x}{225} + \frac{1331 \log{\left (x + \frac{3}{5} \right )}}{125} - \frac{343 \log{\left (x + \frac{2}{3} \right )}}{27} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-4*x**2/15 + 332*x/225 + 1331*log(x + 3/5)/125 - 343*log(x + 2/3)/27

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GIAC/XCAS [A]  time = 0.212261, size = 36, normalized size = 1.09 \[ -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{343}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-4/15*x^2 + 332/225*x + 1331/125*ln(abs(5*x + 3)) - 343/27*ln(abs(3*x + 2))