3.1351 \(\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^5} \, dx\)

Optimal. Leaf size=60 \[ -\frac{200 x}{243}+\frac{8198}{729 (3 x+2)}-\frac{11599}{1458 (3 x+2)^2}+\frac{3724}{2187 (3 x+2)^3}-\frac{343}{2916 (3 x+2)^4}+\frac{2180}{729} \log (3 x+2) \]

[Out]

(-200*x)/243 - 343/(2916*(2 + 3*x)^4) + 3724/(2187*(2 + 3*x)^3) - 11599/(1458*(2
+ 3*x)^2) + 8198/(729*(2 + 3*x)) + (2180*Log[2 + 3*x])/729

_______________________________________________________________________________________

Rubi [A]  time = 0.0678348, antiderivative size = 60, 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 \[ -\frac{200 x}{243}+\frac{8198}{729 (3 x+2)}-\frac{11599}{1458 (3 x+2)^2}+\frac{3724}{2187 (3 x+2)^3}-\frac{343}{2916 (3 x+2)^4}+\frac{2180}{729} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(-200*x)/243 - 343/(2916*(2 + 3*x)^4) + 3724/(2187*(2 + 3*x)^3) - 11599/(1458*(2
+ 3*x)^2) + 8198/(729*(2 + 3*x)) + (2180*Log[2 + 3*x])/729

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{2180 \log{\left (3 x + 2 \right )}}{729} + \int \left (- \frac{200}{243}\right )\, dx + \frac{8198}{729 \left (3 x + 2\right )} - \frac{11599}{1458 \left (3 x + 2\right )^{2}} + \frac{3724}{2187 \left (3 x + 2\right )^{3}} - \frac{343}{2916 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2180*log(3*x + 2)/729 + Integral(-200/243, x) + 8198/(729*(3*x + 2)) - 11599/(14
58*(3*x + 2)**2) + 3724/(2187*(3*x + 2)**3) - 343/(2916*(3*x + 2)**4)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0537143, size = 51, normalized size = 0.85 \[ \frac{-583200 x^5-1944000 x^4+64152 x^3+2957958 x^2+2175096 x+26160 (3 x+2)^4 \log (30 x+20)+460595}{8748 (3 x+2)^4} \]

Antiderivative was successfully verified.

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

[Out]

(460595 + 2175096*x + 2957958*x^2 + 64152*x^3 - 1944000*x^4 - 583200*x^5 + 26160
*(2 + 3*x)^4*Log[20 + 30*x])/(8748*(2 + 3*x)^4)

_______________________________________________________________________________________

Maple [A]  time = 0.01, size = 49, normalized size = 0.8 \[ -{\frac{200\,x}{243}}-{\frac{343}{2916\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{3724}{2187\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{11599}{1458\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{8198}{1458+2187\,x}}+{\frac{2180\,\ln \left ( 2+3\,x \right ) }{729}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-200/243*x-343/2916/(2+3*x)^4+3724/2187/(2+3*x)^3-11599/1458/(2+3*x)^2+8198/729/
(2+3*x)+2180/729*ln(2+3*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34219, size = 69, normalized size = 1.15 \[ -\frac{200}{243} \, x + \frac{2656152 \, x^{3} + 4685958 \, x^{2} + 2751096 \, x + 537395}{8748 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{2180}{729} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-200/243*x + 1/8748*(2656152*x^3 + 4685958*x^2 + 2751096*x + 537395)/(81*x^4 + 2
16*x^3 + 216*x^2 + 96*x + 16) + 2180/729*log(3*x + 2)

_______________________________________________________________________________________

Fricas [A]  time = 0.213393, size = 104, normalized size = 1.73 \[ -\frac{583200 \, x^{5} + 1555200 \, x^{4} - 1100952 \, x^{3} - 3994758 \, x^{2} - 26160 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) - 2635896 \, x - 537395}{8748 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/8748*(583200*x^5 + 1555200*x^4 - 1100952*x^3 - 3994758*x^2 - 26160*(81*x^4 +
216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) - 2635896*x - 537395)/(81*x^4 + 216*
x^3 + 216*x^2 + 96*x + 16)

_______________________________________________________________________________________

Sympy [A]  time = 0.387308, size = 49, normalized size = 0.82 \[ - \frac{200 x}{243} + \frac{2656152 x^{3} + 4685958 x^{2} + 2751096 x + 537395}{708588 x^{4} + 1889568 x^{3} + 1889568 x^{2} + 839808 x + 139968} + \frac{2180 \log{\left (3 x + 2 \right )}}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-200*x/243 + (2656152*x**3 + 4685958*x**2 + 2751096*x + 537395)/(708588*x**4 + 1
889568*x**3 + 1889568*x**2 + 839808*x + 139968) + 2180*log(3*x + 2)/729

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.221619, size = 80, normalized size = 1.33 \[ -\frac{200}{243} \, x + \frac{8198}{729 \,{\left (3 \, x + 2\right )}} - \frac{11599}{1458 \,{\left (3 \, x + 2\right )}^{2}} + \frac{3724}{2187 \,{\left (3 \, x + 2\right )}^{3}} - \frac{343}{2916 \,{\left (3 \, x + 2\right )}^{4}} - \frac{2180}{729} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) - \frac{400}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-200/243*x + 8198/729/(3*x + 2) - 11599/1458/(3*x + 2)^2 + 3724/2187/(3*x + 2)^3
- 343/2916/(3*x + 2)^4 - 2180/729*ln(1/3*abs(3*x + 2)/(3*x + 2)^2) - 400/729