3.1209 \(\int \frac{(1-2 x) (2+3 x)^3}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{27 x^2}{125}+\frac{81 x}{625}-\frac{97}{3125 (5 x+3)}-\frac{11}{6250 (5 x+3)^2}+\frac{279 \log (5 x+3)}{3125} \]

[Out]

(81*x)/625 - (27*x^2)/125 - 11/(6250*(3 + 5*x)^2) - 97/(3125*(3 + 5*x)) + (279*L
og[3 + 5*x])/3125

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Rubi [A]  time = 0.0549708, antiderivative size = 45, 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 \[ -\frac{27 x^2}{125}+\frac{81 x}{625}-\frac{97}{3125 (5 x+3)}-\frac{11}{6250 (5 x+3)^2}+\frac{279 \log (5 x+3)}{3125} \]

Antiderivative was successfully verified.

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

[Out]

(81*x)/625 - (27*x^2)/125 - 11/(6250*(3 + 5*x)^2) - 97/(3125*(3 + 5*x)) + (279*L
og[3 + 5*x])/3125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{279 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{81}{625}\, dx - \frac{54 \int x\, dx}{125} - \frac{97}{3125 \left (5 x + 3\right )} - \frac{11}{6250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

279*log(5*x + 3)/3125 + Integral(81/625, x) - 54*Integral(x, x)/125 - 97/(3125*(
5*x + 3)) - 11/(6250*(5*x + 3)**2)

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Mathematica [A]  time = 0.02146, size = 48, normalized size = 1.07 \[ \frac{-33750 x^4-20250 x^3+40650 x^2+40520 x+558 (5 x+3)^2 \log (-3 (5 x+3))+9667}{6250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(9667 + 40520*x + 40650*x^2 - 20250*x^3 - 33750*x^4 + 558*(3 + 5*x)^2*Log[-3*(3
+ 5*x)])/(6250*(3 + 5*x)^2)

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Maple [A]  time = 0.01, size = 36, normalized size = 0.8 \[{\frac{81\,x}{625}}-{\frac{27\,{x}^{2}}{125}}-{\frac{11}{6250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{97}{9375+15625\,x}}+{\frac{279\,\ln \left ( 3+5\,x \right ) }{3125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81/625*x-27/125*x^2-11/6250/(3+5*x)^2-97/3125/(3+5*x)+279/3125*ln(3+5*x)

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Maxima [A]  time = 1.35294, size = 49, normalized size = 1.09 \[ -\frac{27}{125} \, x^{2} + \frac{81}{625} \, x - \frac{970 \, x + 593}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{279}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/125*x^2 + 81/625*x - 1/6250*(970*x + 593)/(25*x^2 + 30*x + 9) + 279/3125*log
(5*x + 3)

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Fricas [A]  time = 0.224635, size = 70, normalized size = 1.56 \[ -\frac{33750 \, x^{4} + 20250 \, x^{3} - 12150 \, x^{2} - 558 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 6320 \, x + 593}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6250*(33750*x^4 + 20250*x^3 - 12150*x^2 - 558*(25*x^2 + 30*x + 9)*log(5*x + 3
) - 6320*x + 593)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.276765, size = 36, normalized size = 0.8 \[ - \frac{27 x^{2}}{125} + \frac{81 x}{625} - \frac{970 x + 593}{156250 x^{2} + 187500 x + 56250} + \frac{279 \log{\left (5 x + 3 \right )}}{3125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27*x**2/125 + 81*x/625 - (970*x + 593)/(156250*x**2 + 187500*x + 56250) + 279*l
og(5*x + 3)/3125

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GIAC/XCAS [A]  time = 0.208499, size = 43, normalized size = 0.96 \[ -\frac{27}{125} \, x^{2} + \frac{81}{625} \, x - \frac{970 \, x + 593}{6250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{279}{3125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/125*x^2 + 81/625*x - 1/6250*(970*x + 593)/(5*x + 3)^2 + 279/3125*ln(abs(5*x
+ 3))