3.1394 \(\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=43 \[ -\frac{343}{9 (3 x+2)}-\frac{1331}{25 (5 x+3)}+\frac{3136}{9} \log (3 x+2)-\frac{8712}{25} \log (5 x+3) \]

[Out]

-343/(9*(2 + 3*x)) - 1331/(25*(3 + 5*x)) + (3136*Log[2 + 3*x])/9 - (8712*Log[3 +
5*x])/25

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Rubi [A]  time = 0.0497177, antiderivative size = 43, 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 \[ -\frac{343}{9 (3 x+2)}-\frac{1331}{25 (5 x+3)}+\frac{3136}{9} \log (3 x+2)-\frac{8712}{25} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-343/(9*(2 + 3*x)) - 1331/(25*(3 + 5*x)) + (3136*Log[2 + 3*x])/9 - (8712*Log[3 +
5*x])/25

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Rubi in Sympy [A]  time = 3.59895, size = 32, normalized size = 0.74 \[ \frac{3136 \log{\left (3 x + 2 \right )}}{9} - \frac{8712 \log{\left (5 x + 3 \right )}}{25} - \frac{1331}{25 \left (5 x + 3\right )} - \frac{343}{9 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3136*log(3*x + 2)/9 - 8712*log(5*x + 3)/25 - 1331/(25*(5*x + 3)) - 343/(9*(3*x +
2))

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Mathematica [A]  time = 0.0452626, size = 61, normalized size = 1.42 \[ -\frac{-78400 \left (15 x^2+19 x+6\right ) \log (5 (3 x+2))+78408 \left (15 x^2+19 x+6\right ) \log (5 x+3)+78812 x+49683}{225 (3 x+2) (5 x+3)} \]

Antiderivative was successfully verified.

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

[Out]

-(49683 + 78812*x - 78400*(6 + 19*x + 15*x^2)*Log[5*(2 + 3*x)] + 78408*(6 + 19*x
+ 15*x^2)*Log[3 + 5*x])/(225*(2 + 3*x)*(3 + 5*x))

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Maple [A]  time = 0.015, size = 36, normalized size = 0.8 \[ -{\frac{343}{18+27\,x}}-{\frac{1331}{75+125\,x}}+{\frac{3136\,\ln \left ( 2+3\,x \right ) }{9}}-{\frac{8712\,\ln \left ( 3+5\,x \right ) }{25}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-343/9/(2+3*x)-1331/25/(3+5*x)+3136/9*ln(2+3*x)-8712/25*ln(3+5*x)

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Maxima [A]  time = 1.32563, size = 49, normalized size = 1.14 \[ -\frac{78812 \, x + 49683}{225 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} - \frac{8712}{25} \, \log \left (5 \, x + 3\right ) + \frac{3136}{9} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/225*(78812*x + 49683)/(15*x^2 + 19*x + 6) - 8712/25*log(5*x + 3) + 3136/9*log
(3*x + 2)

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Fricas [A]  time = 0.219204, size = 74, normalized size = 1.72 \[ -\frac{78408 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 78400 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 78812 \, x + 49683}{225 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/225*(78408*(15*x^2 + 19*x + 6)*log(5*x + 3) - 78400*(15*x^2 + 19*x + 6)*log(3
*x + 2) + 78812*x + 49683)/(15*x^2 + 19*x + 6)

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Sympy [A]  time = 0.380732, size = 34, normalized size = 0.79 \[ - \frac{78812 x + 49683}{3375 x^{2} + 4275 x + 1350} - \frac{8712 \log{\left (x + \frac{3}{5} \right )}}{25} + \frac{3136 \log{\left (x + \frac{2}{3} \right )}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(78812*x + 49683)/(3375*x**2 + 4275*x + 1350) - 8712*log(x + 3/5)/25 + 3136*log
(x + 2/3)/9

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GIAC/XCAS [A]  time = 0.218148, size = 76, normalized size = 1.77 \[ -\frac{1331}{25 \,{\left (5 \, x + 3\right )}} + \frac{1715}{3 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}} + \frac{8}{225} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{3136}{9} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1331/25/(5*x + 3) + 1715/3/(1/(5*x + 3) + 3) + 8/225*ln(1/5*abs(5*x + 3)/(5*x +
3)^2) + 3136/9*ln(abs(-1/(5*x + 3) - 3))