3.1408 \(\int \frac{(1-2 x)^3}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=38 \[ -\frac{8 x}{125}+\frac{726}{625 (5 x+3)}-\frac{1331}{1250 (5 x+3)^2}+\frac{132}{625} \log (5 x+3) \]

[Out]

(-8*x)/125 - 1331/(1250*(3 + 5*x)^2) + 726/(625*(3 + 5*x)) + (132*Log[3 + 5*x])/
625

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Rubi [A]  time = 0.0359261, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{8 x}{125}+\frac{726}{625 (5 x+3)}-\frac{1331}{1250 (5 x+3)^2}+\frac{132}{625} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3/(3 + 5*x)^3,x]

[Out]

(-8*x)/125 - 1331/(1250*(3 + 5*x)^2) + 726/(625*(3 + 5*x)) + (132*Log[3 + 5*x])/
625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{132 \log{\left (5 x + 3 \right )}}{625} + \int \left (- \frac{8}{125}\right )\, dx + \frac{726}{625 \left (5 x + 3\right )} - \frac{1331}{1250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

132*log(5*x + 3)/625 + Integral(-8/125, x) + 726/(625*(5*x + 3)) - 1331/(1250*(5
*x + 3)**2)

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Mathematica [A]  time = 0.026445, size = 37, normalized size = 0.97 \[ \frac{\frac{5 \left (-400 x^3-280 x^2+1548 x+677\right )}{(5 x+3)^2}+264 \log (10 x+6)}{1250} \]

Antiderivative was successfully verified.

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

[Out]

((5*(677 + 1548*x - 280*x^2 - 400*x^3))/(3 + 5*x)^2 + 264*Log[6 + 10*x])/1250

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Maple [A]  time = 0.009, size = 31, normalized size = 0.8 \[ -{\frac{8\,x}{125}}-{\frac{1331}{1250\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{726}{1875+3125\,x}}+{\frac{132\,\ln \left ( 3+5\,x \right ) }{625}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3/(3+5*x)^3,x)

[Out]

-8/125*x-1331/1250/(3+5*x)^2+726/625/(3+5*x)+132/625*ln(3+5*x)

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Maxima [A]  time = 1.34521, size = 42, normalized size = 1.11 \[ -\frac{8}{125} \, x + \frac{121 \,{\left (12 \, x + 5\right )}}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{132}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/125*x + 121/250*(12*x + 5)/(25*x^2 + 30*x + 9) + 132/625*log(5*x + 3)

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Fricas [A]  time = 0.221115, size = 63, normalized size = 1.66 \[ -\frac{2000 \, x^{3} + 2400 \, x^{2} - 264 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 6540 \, x - 3025}{1250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1250*(2000*x^3 + 2400*x^2 - 264*(25*x^2 + 30*x + 9)*log(5*x + 3) - 6540*x - 3
025)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.245763, size = 29, normalized size = 0.76 \[ - \frac{8 x}{125} + \frac{1452 x + 605}{6250 x^{2} + 7500 x + 2250} + \frac{132 \log{\left (5 x + 3 \right )}}{625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x/125 + (1452*x + 605)/(6250*x**2 + 7500*x + 2250) + 132*log(5*x + 3)/625

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GIAC/XCAS [A]  time = 0.20854, size = 36, normalized size = 0.95 \[ -\frac{8}{125} \, x + \frac{121 \,{\left (12 \, x + 5\right )}}{250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{132}{625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/125*x + 121/250*(12*x + 5)/(5*x + 3)^2 + 132/625*ln(abs(5*x + 3))