3.1311 \(\int \frac{(1-2 x)^2 (2+3 x)}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=38 \[ \frac{12 x}{125}-\frac{319}{625 (5 x+3)}-\frac{121}{1250 (5 x+3)^2}-\frac{128}{625} \log (5 x+3) \]

[Out]

(12*x)/125 - 121/(1250*(3 + 5*x)^2) - 319/(625*(3 + 5*x)) - (128*Log[3 + 5*x])/6
25

_______________________________________________________________________________________

Rubi [A]  time = 0.0466938, 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 \[ \frac{12 x}{125}-\frac{319}{625 (5 x+3)}-\frac{121}{1250 (5 x+3)^2}-\frac{128}{625} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(12*x)/125 - 121/(1250*(3 + 5*x)^2) - 319/(625*(3 + 5*x)) - (128*Log[3 + 5*x])/6
25

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{128 \log{\left (5 x + 3 \right )}}{625} + \int \frac{12}{125}\, dx - \frac{319}{625 \left (5 x + 3\right )} - \frac{121}{1250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-128*log(5*x + 3)/625 + Integral(12/125, x) - 319/(625*(5*x + 3)) - 121/(1250*(5
*x + 3)**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0267467, size = 37, normalized size = 0.97 \[ \frac{\frac{5 \left (600 x^3+420 x^2-782 x-515\right )}{(5 x+3)^2}-256 \log (10 x+6)}{1250} \]

Antiderivative was successfully verified.

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

[Out]

((5*(-515 - 782*x + 420*x^2 + 600*x^3))/(3 + 5*x)^2 - 256*Log[6 + 10*x])/1250

_______________________________________________________________________________________

Maple [A]  time = 0.009, size = 31, normalized size = 0.8 \[{\frac{12\,x}{125}}-{\frac{121}{1250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{319}{1875+3125\,x}}-{\frac{128\,\ln \left ( 3+5\,x \right ) }{625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12/125*x-121/1250/(3+5*x)^2-319/625/(3+5*x)-128/625*ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.35592, size = 42, normalized size = 1.11 \[ \frac{12}{125} \, x - \frac{11 \,{\left (58 \, x + 37\right )}}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{128}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12/125*x - 11/250*(58*x + 37)/(25*x^2 + 30*x + 9) - 128/625*log(5*x + 3)

_______________________________________________________________________________________

Fricas [A]  time = 0.207649, size = 63, normalized size = 1.66 \[ \frac{3000 \, x^{3} + 3600 \, x^{2} - 256 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 2110 \, x - 2035}{1250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1250*(3000*x^3 + 3600*x^2 - 256*(25*x^2 + 30*x + 9)*log(5*x + 3) - 2110*x - 20
35)/(25*x^2 + 30*x + 9)

_______________________________________________________________________________________

Sympy [A]  time = 0.265727, size = 29, normalized size = 0.76 \[ \frac{12 x}{125} - \frac{638 x + 407}{6250 x^{2} + 7500 x + 2250} - \frac{128 \log{\left (5 x + 3 \right )}}{625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12*x/125 - (638*x + 407)/(6250*x**2 + 7500*x + 2250) - 128*log(5*x + 3)/625

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.205795, size = 36, normalized size = 0.95 \[ \frac{12}{125} \, x - \frac{11 \,{\left (58 \, x + 37\right )}}{250 \,{\left (5 \, x + 3\right )}^{2}} - \frac{128}{625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

12/125*x - 11/250*(58*x + 37)/(5*x + 3)^2 - 128/625*ln(abs(5*x + 3))