3.1393 \(\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)^2} \, dx\)

Optimal. Leaf size=37 \[ -\frac{8 x}{75}-\frac{1331}{125 (5 x+3)}+\frac{343}{9} \log (3 x+2)-\frac{4719}{125} \log (5 x+3) \]

[Out]

(-8*x)/75 - 1331/(125*(3 + 5*x)) + (343*Log[2 + 3*x])/9 - (4719*Log[3 + 5*x])/12
5

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Rubi [A]  time = 0.0464686, antiderivative size = 37, 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 \[ -\frac{8 x}{75}-\frac{1331}{125 (5 x+3)}+\frac{343}{9} \log (3 x+2)-\frac{4719}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(-8*x)/75 - 1331/(125*(3 + 5*x)) + (343*Log[2 + 3*x])/9 - (4719*Log[3 + 5*x])/12
5

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{343 \log{\left (3 x + 2 \right )}}{9} - \frac{4719 \log{\left (5 x + 3 \right )}}{125} + \int \left (- \frac{8}{75}\right )\, dx - \frac{1331}{125 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343*log(3*x + 2)/9 - 4719*log(5*x + 3)/125 + Integral(-8/75, x) - 1331/(125*(5*x
+ 3))

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Mathematica [A]  time = 0.0358256, size = 36, normalized size = 0.97 \[ \frac{-120 x-\frac{11979}{5 x+3}+42875 \log (3 x+2)-42471 \log (-3 (5 x+3))-80}{1125} \]

Antiderivative was successfully verified.

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

[Out]

(-80 - 120*x - 11979/(3 + 5*x) + 42875*Log[2 + 3*x] - 42471*Log[-3*(3 + 5*x)])/1
125

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Maple [A]  time = 0.011, size = 30, normalized size = 0.8 \[ -{\frac{8\,x}{75}}-{\frac{1331}{375+625\,x}}+{\frac{343\,\ln \left ( 2+3\,x \right ) }{9}}-{\frac{4719\,\ln \left ( 3+5\,x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/75*x-1331/125/(3+5*x)+343/9*ln(2+3*x)-4719/125*ln(3+5*x)

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Maxima [A]  time = 1.32058, size = 39, normalized size = 1.05 \[ -\frac{8}{75} \, x - \frac{1331}{125 \,{\left (5 \, x + 3\right )}} - \frac{4719}{125} \, \log \left (5 \, x + 3\right ) + \frac{343}{9} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/75*x - 1331/125/(5*x + 3) - 4719/125*log(5*x + 3) + 343/9*log(3*x + 2)

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Fricas [A]  time = 0.208845, size = 61, normalized size = 1.65 \[ -\frac{600 \, x^{2} + 42471 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 42875 \,{\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 360 \, x + 11979}{1125 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1125*(600*x^2 + 42471*(5*x + 3)*log(5*x + 3) - 42875*(5*x + 3)*log(3*x + 2) +
360*x + 11979)/(5*x + 3)

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Sympy [A]  time = 0.334, size = 31, normalized size = 0.84 \[ - \frac{8 x}{75} - \frac{4719 \log{\left (x + \frac{3}{5} \right )}}{125} + \frac{343 \log{\left (x + \frac{2}{3} \right )}}{9} - \frac{1331}{625 x + 375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x/75 - 4719*log(x + 3/5)/125 + 343*log(x + 2/3)/9 - 1331/(625*x + 375)

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GIAC/XCAS [A]  time = 0.217821, size = 63, normalized size = 1.7 \[ -\frac{8}{75} \, x - \frac{1331}{125 \,{\left (5 \, x + 3\right )}} - \frac{404}{1125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{343}{9} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{8}{125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/75*x - 1331/125/(5*x + 3) - 404/1125*ln(1/5*abs(5*x + 3)/(5*x + 3)^2) + 343/9
*ln(abs(-1/(5*x + 3) - 3)) - 8/125