3.1309 \(\int \frac{(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=52 \[ \frac{36 x^3}{125}-\frac{216 x^2}{625}-\frac{153 x}{3125}-\frac{209}{3125 (5 x+3)}-\frac{121}{31250 (5 x+3)^2}+\frac{23}{125} \log (5 x+3) \]

[Out]

(-153*x)/3125 - (216*x^2)/625 + (36*x^3)/125 - 121/(31250*(3 + 5*x)^2) - 209/(31
25*(3 + 5*x)) + (23*Log[3 + 5*x])/125

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Rubi [A]  time = 0.067935, antiderivative size = 52, 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 \[ \frac{36 x^3}{125}-\frac{216 x^2}{625}-\frac{153 x}{3125}-\frac{209}{3125 (5 x+3)}-\frac{121}{31250 (5 x+3)^2}+\frac{23}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(-153*x)/3125 - (216*x^2)/625 + (36*x^3)/125 - 121/(31250*(3 + 5*x)^2) - 209/(31
25*(3 + 5*x)) + (23*Log[3 + 5*x])/125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{36 x^{3}}{125} + \frac{23 \log{\left (5 x + 3 \right )}}{125} + \int \left (- \frac{153}{3125}\right )\, dx - \frac{432 \int x\, dx}{625} - \frac{209}{3125 \left (5 x + 3\right )} - \frac{121}{31250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

36*x**3/125 + 23*log(5*x + 3)/125 + Integral(-153/3125, x) - 432*Integral(x, x)/
625 - 209/(3125*(5*x + 3)) - 121/(31250*(5*x + 3)**2)

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Mathematica [A]  time = 0.0515377, size = 48, normalized size = 0.92 \[ \frac{45000 x^5-56250 x^3-4050 x^2+24640 x+1150 (5 x+3)^2 \log (6 (5 x+3))+7567}{6250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(7567 + 24640*x - 4050*x^2 - 56250*x^3 + 45000*x^5 + 1150*(3 + 5*x)^2*Log[6*(3 +
5*x)])/(6250*(3 + 5*x)^2)

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Maple [A]  time = 0.01, size = 41, normalized size = 0.8 \[ -{\frac{153\,x}{3125}}-{\frac{216\,{x}^{2}}{625}}+{\frac{36\,{x}^{3}}{125}}-{\frac{121}{31250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{209}{9375+15625\,x}}+{\frac{23\,\ln \left ( 3+5\,x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-153/3125*x-216/625*x^2+36/125*x^3-121/31250/(3+5*x)^2-209/3125/(3+5*x)+23/125*l
n(3+5*x)

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Maxima [A]  time = 1.33153, size = 55, normalized size = 1.06 \[ \frac{36}{125} \, x^{3} - \frac{216}{625} \, x^{2} - \frac{153}{3125} \, x - \frac{11 \,{\left (950 \, x + 581\right )}}{31250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{23}{125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

36/125*x^3 - 216/625*x^2 - 153/3125*x - 11/31250*(950*x + 581)/(25*x^2 + 30*x +
9) + 23/125*log(5*x + 3)

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Fricas [A]  time = 0.217841, size = 70, normalized size = 1.35 \[ \frac{225000 \, x^{5} - 281250 \, x^{3} - 143100 \, x^{2} + 5750 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 24220 \, x - 6391}{31250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/31250*(225000*x^5 - 281250*x^3 - 143100*x^2 + 5750*(25*x^2 + 30*x + 9)*log(5*x
+ 3) - 24220*x - 6391)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.276127, size = 42, normalized size = 0.81 \[ \frac{36 x^{3}}{125} - \frac{216 x^{2}}{625} - \frac{153 x}{3125} - \frac{10450 x + 6391}{781250 x^{2} + 937500 x + 281250} + \frac{23 \log{\left (5 x + 3 \right )}}{125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

36*x**3/125 - 216*x**2/625 - 153*x/3125 - (10450*x + 6391)/(781250*x**2 + 937500
*x + 281250) + 23*log(5*x + 3)/125

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GIAC/XCAS [A]  time = 0.212945, size = 50, normalized size = 0.96 \[ \frac{36}{125} \, x^{3} - \frac{216}{625} \, x^{2} - \frac{153}{3125} \, x - \frac{11 \,{\left (950 \, x + 581\right )}}{31250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{23}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

36/125*x^3 - 216/625*x^2 - 153/3125*x - 11/31250*(950*x + 581)/(5*x + 3)^2 + 23/
125*ln(abs(5*x + 3))