3.1210 \(\int \frac{(1-2 x) (2+3 x)^2}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=38 \[ -\frac{18 x}{125}-\frac{64}{625 (5 x+3)}-\frac{11}{1250 (5 x+3)^2}+\frac{87}{625} \log (5 x+3) \]

[Out]

(-18*x)/125 - 11/(1250*(3 + 5*x)^2) - 64/(625*(3 + 5*x)) + (87*Log[3 + 5*x])/625

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Rubi [A]  time = 0.0472724, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{18 x}{125}-\frac{64}{625 (5 x+3)}-\frac{11}{1250 (5 x+3)^2}+\frac{87}{625} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(-18*x)/125 - 11/(1250*(3 + 5*x)^2) - 64/(625*(3 + 5*x)) + (87*Log[3 + 5*x])/625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{87 \log{\left (5 x + 3 \right )}}{625} + \int \left (- \frac{18}{125}\right )\, dx - \frac{64}{625 \left (5 x + 3\right )} - \frac{11}{1250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

87*log(5*x + 3)/625 + Integral(-18/125, x) - 64/(625*(5*x + 3)) - 11/(1250*(5*x
+ 3)**2)

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Mathematica [A]  time = 0.0276094, size = 39, normalized size = 1.03 \[ \frac{87}{625} \log (-3 (5 x+3))-\frac{900 x^3+1680 x^2+1172 x+295}{250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

-(295 + 1172*x + 1680*x^2 + 900*x^3)/(250*(3 + 5*x)^2) + (87*Log[-3*(3 + 5*x)])/
625

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Maple [A]  time = 0.008, size = 31, normalized size = 0.8 \[ -{\frac{18\,x}{125}}-{\frac{11}{1250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{64}{1875+3125\,x}}+{\frac{87\,\ln \left ( 3+5\,x \right ) }{625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18/125*x-11/1250/(3+5*x)^2-64/625/(3+5*x)+87/625*ln(3+5*x)

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Maxima [A]  time = 1.40266, size = 42, normalized size = 1.11 \[ -\frac{18}{125} \, x - \frac{128 \, x + 79}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{87}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18/125*x - 1/250*(128*x + 79)/(25*x^2 + 30*x + 9) + 87/625*log(5*x + 3)

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Fricas [A]  time = 0.220602, size = 63, normalized size = 1.66 \[ -\frac{4500 \, x^{3} + 5400 \, x^{2} - 174 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2260 \, x + 395}{1250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1250*(4500*x^3 + 5400*x^2 - 174*(25*x^2 + 30*x + 9)*log(5*x + 3) + 2260*x + 3
95)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.266315, size = 29, normalized size = 0.76 \[ - \frac{18 x}{125} - \frac{128 x + 79}{6250 x^{2} + 7500 x + 2250} + \frac{87 \log{\left (5 x + 3 \right )}}{625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18*x/125 - (128*x + 79)/(6250*x**2 + 7500*x + 2250) + 87*log(5*x + 3)/625

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GIAC/XCAS [A]  time = 0.212871, size = 36, normalized size = 0.95 \[ -\frac{18}{125} \, x - \frac{128 \, x + 79}{250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{87}{625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-18/125*x - 1/250*(128*x + 79)/(5*x + 3)^2 + 87/625*ln(abs(5*x + 3))