3.1409 \(\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)^3} \, dx\)

Optimal. Leaf size=43 \[ \frac{4719}{125 (5 x+3)}-\frac{1331}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2)+\frac{14289}{125} \log (5 x+3) \]

[Out]

-1331/(250*(3 + 5*x)^2) + 4719/(125*(3 + 5*x)) - (343*Log[2 + 3*x])/3 + (14289*L
og[3 + 5*x])/125

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Rubi [A]  time = 0.0496146, 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 \[ \frac{4719}{125 (5 x+3)}-\frac{1331}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2)+\frac{14289}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-1331/(250*(3 + 5*x)^2) + 4719/(125*(3 + 5*x)) - (343*Log[2 + 3*x])/3 + (14289*L
og[3 + 5*x])/125

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Rubi in Sympy [A]  time = 7.42212, size = 36, normalized size = 0.84 \[ - \frac{343 \log{\left (3 x + 2 \right )}}{3} + \frac{14289 \log{\left (5 x + 3 \right )}}{125} + \frac{4719}{125 \left (5 x + 3\right )} - \frac{1331}{250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-343*log(3*x + 2)/3 + 14289*log(5*x + 3)/125 + 4719/(125*(5*x + 3)) - 1331/(250*
(5*x + 3)**2)

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Mathematica [A]  time = 0.0394622, size = 44, normalized size = 1.02 \[ \frac{11 \left (4290 x+2598 (5 x+3)^2 \log (-3 (5 x+3))+2453\right )}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(-343*Log[2 + 3*x])/3 + (11*(2453 + 4290*x + 2598*(3 + 5*x)^2*Log[-3*(3 + 5*x)])
)/(250*(3 + 5*x)^2)

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Maple [A]  time = 0.012, size = 36, normalized size = 0.8 \[ -{\frac{1331}{250\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{4719}{375+625\,x}}-{\frac{343\,\ln \left ( 2+3\,x \right ) }{3}}+{\frac{14289\,\ln \left ( 3+5\,x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1331/250/(3+5*x)^2+4719/125/(3+5*x)-343/3*ln(2+3*x)+14289/125*ln(3+5*x)

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Maxima [A]  time = 1.42455, size = 49, normalized size = 1.14 \[ \frac{121 \,{\left (390 \, x + 223\right )}}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{14289}{125} \, \log \left (5 \, x + 3\right ) - \frac{343}{3} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121/250*(390*x + 223)/(25*x^2 + 30*x + 9) + 14289/125*log(5*x + 3) - 343/3*log(3
*x + 2)

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Fricas [A]  time = 0.22425, size = 74, normalized size = 1.72 \[ \frac{85734 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 85750 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 141570 \, x + 80949}{750 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/750*(85734*(25*x^2 + 30*x + 9)*log(5*x + 3) - 85750*(25*x^2 + 30*x + 9)*log(3*
x + 2) + 141570*x + 80949)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.38457, size = 34, normalized size = 0.79 \[ \frac{47190 x + 26983}{6250 x^{2} + 7500 x + 2250} + \frac{14289 \log{\left (x + \frac{3}{5} \right )}}{125} - \frac{343 \log{\left (x + \frac{2}{3} \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(47190*x + 26983)/(6250*x**2 + 7500*x + 2250) + 14289*log(x + 3/5)/125 - 343*log
(x + 2/3)/3

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GIAC/XCAS [A]  time = 0.210784, size = 45, normalized size = 1.05 \[ \frac{121 \,{\left (390 \, x + 223\right )}}{250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{14289}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{343}{3} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121/250*(390*x + 223)/(5*x + 3)^2 + 14289/125*ln(abs(5*x + 3)) - 343/3*ln(abs(3*
x + 2))