3.1407 \(\int \frac{(1-2 x)^3 (2+3 x)}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{12 x^2}{125}+\frac{316 x}{625}-\frac{3267}{3125 (5 x+3)}-\frac{1331}{6250 (5 x+3)^2}-\frac{2046 \log (5 x+3)}{3125} \]

[Out]

(316*x)/625 - (12*x^2)/125 - 1331/(6250*(3 + 5*x)^2) - 3267/(3125*(3 + 5*x)) - (
2046*Log[3 + 5*x])/3125

_______________________________________________________________________________________

Rubi [A]  time = 0.0547491, 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 \[ -\frac{12 x^2}{125}+\frac{316 x}{625}-\frac{3267}{3125 (5 x+3)}-\frac{1331}{6250 (5 x+3)^2}-\frac{2046 \log (5 x+3)}{3125} \]

Antiderivative was successfully verified.

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

[Out]

(316*x)/625 - (12*x^2)/125 - 1331/(6250*(3 + 5*x)^2) - 3267/(3125*(3 + 5*x)) - (
2046*Log[3 + 5*x])/3125

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{2046 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{316}{625}\, dx - \frac{24 \int x\, dx}{125} - \frac{3267}{3125 \left (5 x + 3\right )} - \frac{1331}{6250 \left (5 x + 3\right )^{2}} \]

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]

-2046*log(5*x + 3)/3125 + Integral(316/625, x) - 24*Integral(x, x)/125 - 3267/(3
125*(5*x + 3)) - 1331/(6250*(5*x + 3)**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0277076, size = 46, normalized size = 1.02 \[ -\frac{15000 x^4-61000 x^3-53650 x^2+47130 x+4092 (5 x+3)^2 \log (10 x+6)+33803}{6250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

-(33803 + 47130*x - 53650*x^2 - 61000*x^3 + 15000*x^4 + 4092*(3 + 5*x)^2*Log[6 +
10*x])/(6250*(3 + 5*x)^2)

_______________________________________________________________________________________

Maple [A]  time = 0.01, size = 36, normalized size = 0.8 \[{\frac{316\,x}{625}}-{\frac{12\,{x}^{2}}{125}}-{\frac{1331}{6250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{3267}{9375+15625\,x}}-{\frac{2046\,\ln \left ( 3+5\,x \right ) }{3125}} \]

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]

316/625*x-12/125*x^2-1331/6250/(3+5*x)^2-3267/3125/(3+5*x)-2046/3125*ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.32993, size = 49, normalized size = 1.09 \[ -\frac{12}{125} \, x^{2} + \frac{316}{625} \, x - \frac{121 \,{\left (270 \, x + 173\right )}}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{2046}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-12/125*x^2 + 316/625*x - 121/6250*(270*x + 173)/(25*x^2 + 30*x + 9) - 2046/3125
*log(5*x + 3)

_______________________________________________________________________________________

Fricas [A]  time = 0.208864, size = 70, normalized size = 1.56 \[ -\frac{15000 \, x^{4} - 61000 \, x^{3} - 89400 \, x^{2} + 4092 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 4230 \, x + 20933}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6250*(15000*x^4 - 61000*x^3 - 89400*x^2 + 4092*(25*x^2 + 30*x + 9)*log(5*x +
3) + 4230*x + 20933)/(25*x^2 + 30*x + 9)

_______________________________________________________________________________________

Sympy [A]  time = 0.269583, size = 36, normalized size = 0.8 \[ - \frac{12 x^{2}}{125} + \frac{316 x}{625} - \frac{32670 x + 20933}{156250 x^{2} + 187500 x + 56250} - \frac{2046 \log{\left (5 x + 3 \right )}}{3125} \]

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]

-12*x**2/125 + 316*x/625 - (32670*x + 20933)/(156250*x**2 + 187500*x + 56250) -
2046*log(5*x + 3)/3125

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.208803, size = 43, normalized size = 0.96 \[ -\frac{12}{125} \, x^{2} + \frac{316}{625} \, x - \frac{121 \,{\left (270 \, x + 173\right )}}{6250 \,{\left (5 \, x + 3\right )}^{2}} - \frac{2046}{3125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-12/125*x^2 + 316/625*x - 121/6250*(270*x + 173)/(5*x + 3)^2 - 2046/3125*ln(abs(
5*x + 3))