3.1379 \(\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=37 \[ -\frac{8 x}{45}+\frac{343}{27 (3 x+2)}-\frac{1421}{27} \log (3 x+2)+\frac{1331}{25} \log (5 x+3) \]

[Out]

(-8*x)/45 + 343/(27*(2 + 3*x)) - (1421*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/25

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Rubi [A]  time = 0.0458875, 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 \[ -\frac{8 x}{45}+\frac{343}{27 (3 x+2)}-\frac{1421}{27} \log (3 x+2)+\frac{1331}{25} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(-8*x)/45 + 343/(27*(2 + 3*x)) - (1421*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/25

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{1421 \log{\left (3 x + 2 \right )}}{27} + \frac{1331 \log{\left (5 x + 3 \right )}}{25} + \int \left (- \frac{8}{45}\right )\, dx + \frac{343}{27 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1421*log(3*x + 2)/27 + 1331*log(5*x + 3)/25 + Integral(-8/45, x) + 343/(27*(3*x
+ 2))

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Mathematica [A]  time = 0.035138, size = 36, normalized size = 0.97 \[ \frac{1}{675} \left (-120 x+\frac{8575}{3 x+2}-35525 \log (5 (3 x+2))+35937 \log (5 x+3)-72\right ) \]

Antiderivative was successfully verified.

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

[Out]

(-72 - 120*x + 8575/(2 + 3*x) - 35525*Log[5*(2 + 3*x)] + 35937*Log[3 + 5*x])/675

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Maple [A]  time = 0.011, size = 30, normalized size = 0.8 \[ -{\frac{8\,x}{45}}+{\frac{343}{54+81\,x}}-{\frac{1421\,\ln \left ( 2+3\,x \right ) }{27}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{25}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/45*x+343/27/(2+3*x)-1421/27*ln(2+3*x)+1331/25*ln(3+5*x)

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Maxima [A]  time = 1.3418, size = 39, normalized size = 1.05 \[ -\frac{8}{45} \, x + \frac{343}{27 \,{\left (3 \, x + 2\right )}} + \frac{1331}{25} \, \log \left (5 \, x + 3\right ) - \frac{1421}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/45*x + 343/27/(3*x + 2) + 1331/25*log(5*x + 3) - 1421/27*log(3*x + 2)

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Fricas [A]  time = 0.213701, size = 61, normalized size = 1.65 \[ -\frac{360 \, x^{2} - 35937 \,{\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) + 35525 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 240 \, x - 8575}{675 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/675*(360*x^2 - 35937*(3*x + 2)*log(5*x + 3) + 35525*(3*x + 2)*log(3*x + 2) +
240*x - 8575)/(3*x + 2)

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Sympy [A]  time = 0.358191, size = 31, normalized size = 0.84 \[ - \frac{8 x}{45} + \frac{1331 \log{\left (x + \frac{3}{5} \right )}}{25} - \frac{1421 \log{\left (x + \frac{2}{3} \right )}}{27} + \frac{343}{81 x + 54} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x/45 + 1331*log(x + 3/5)/25 - 1421*log(x + 2/3)/27 + 343/(81*x + 54)

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GIAC/XCAS [A]  time = 0.214472, size = 63, normalized size = 1.7 \[ -\frac{8}{45} \, x + \frac{343}{27 \,{\left (3 \, x + 2\right )}} - \frac{412}{675} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) + \frac{1331}{25} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{16}{135} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/45*x + 343/27/(3*x + 2) - 412/675*ln(1/3*abs(3*x + 2)/(3*x + 2)^2) + 1331/25*
ln(abs(-1/(3*x + 2) + 5)) - 16/135