3.1170 \(\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx\)

Optimal. Leaf size=49 \[ -\frac{250 x}{81}+\frac{185}{81 (3 x+2)}-\frac{107}{486 (3 x+2)^2}+\frac{7}{729 (3 x+2)^3}+\frac{1025}{243} \log (3 x+2) \]

[Out]

(-250*x)/81 + 7/(729*(2 + 3*x)^3) - 107/(486*(2 + 3*x)^2) + 185/(81*(2 + 3*x)) +
(1025*Log[2 + 3*x])/243

_______________________________________________________________________________________

Rubi [A]  time = 0.0567237, antiderivative size = 49, 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 \[ -\frac{250 x}{81}+\frac{185}{81 (3 x+2)}-\frac{107}{486 (3 x+2)^2}+\frac{7}{729 (3 x+2)^3}+\frac{1025}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^4,x]

[Out]

(-250*x)/81 + 7/(729*(2 + 3*x)^3) - 107/(486*(2 + 3*x)^2) + 185/(81*(2 + 3*x)) +
(1025*Log[2 + 3*x])/243

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{1025 \log{\left (3 x + 2 \right )}}{243} + \int \left (- \frac{250}{81}\right )\, dx + \frac{185}{81 \left (3 x + 2\right )} - \frac{107}{486 \left (3 x + 2\right )^{2}} + \frac{7}{729 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(3+5*x)**3/(2+3*x)**4,x)

[Out]

1025*log(3*x + 2)/243 + Integral(-250/81, x) + 185/(81*(3*x + 2)) - 107/(486*(3*
x + 2)**2) + 7/(729*(3*x + 2)**3)

_______________________________________________________________________________________

Mathematica [A]  time = 0.030672, size = 47, normalized size = 0.96 \[ \frac{-1500 (3 x+2)+\frac{3330}{3 x+2}-\frac{321}{(3 x+2)^2}+\frac{14}{(3 x+2)^3}+6150 \log (3 x+2)}{1458} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^4,x]

[Out]

(14/(2 + 3*x)^3 - 321/(2 + 3*x)^2 + 3330/(2 + 3*x) - 1500*(2 + 3*x) + 6150*Log[2
+ 3*x])/1458

_______________________________________________________________________________________

Maple [A]  time = 0.008, size = 40, normalized size = 0.8 \[ -{\frac{250\,x}{81}}+{\frac{7}{729\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{107}{486\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{185}{162+243\,x}}+{\frac{1025\,\ln \left ( 2+3\,x \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)^3/(2+3*x)^4,x)

[Out]

-250/81*x+7/729/(2+3*x)^3-107/486/(2+3*x)^2+185/81/(2+3*x)+1025/243*ln(2+3*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.3379, size = 55, normalized size = 1.12 \[ -\frac{250}{81} \, x + \frac{29970 \, x^{2} + 38997 \, x + 12692}{1458 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{1025}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^4,x, algorithm="maxima")

[Out]

-250/81*x + 1/1458*(29970*x^2 + 38997*x + 12692)/(27*x^3 + 54*x^2 + 36*x + 8) +
1025/243*log(3*x + 2)

_______________________________________________________________________________________

Fricas [A]  time = 0.212145, size = 84, normalized size = 1.71 \[ -\frac{121500 \, x^{4} + 243000 \, x^{3} + 132030 \, x^{2} - 6150 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 2997 \, x - 12692}{1458 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^4,x, algorithm="fricas")

[Out]

-1/1458*(121500*x^4 + 243000*x^3 + 132030*x^2 - 6150*(27*x^3 + 54*x^2 + 36*x + 8
)*log(3*x + 2) - 2997*x - 12692)/(27*x^3 + 54*x^2 + 36*x + 8)

_______________________________________________________________________________________

Sympy [A]  time = 0.316763, size = 39, normalized size = 0.8 \[ - \frac{250 x}{81} + \frac{29970 x^{2} + 38997 x + 12692}{39366 x^{3} + 78732 x^{2} + 52488 x + 11664} + \frac{1025 \log{\left (3 x + 2 \right )}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x)**3/(2+3*x)**4,x)

[Out]

-250*x/81 + (29970*x**2 + 38997*x + 12692)/(39366*x**3 + 78732*x**2 + 52488*x +
11664) + 1025*log(3*x + 2)/243

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.213336, size = 43, normalized size = 0.88 \[ -\frac{250}{81} \, x + \frac{29970 \, x^{2} + 38997 \, x + 12692}{1458 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1025}{243} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^4,x, algorithm="giac")

[Out]

-250/81*x + 1/1458*(29970*x^2 + 38997*x + 12692)/(3*x + 2)^3 + 1025/243*ln(abs(3
*x + 2))