3.1352 \(\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^6} \, dx\)

Optimal. Leaf size=66 \[ -\frac{2180}{729 (3 x+2)}+\frac{4099}{729 (3 x+2)^2}-\frac{11599}{2187 (3 x+2)^3}+\frac{931}{729 (3 x+2)^4}-\frac{343}{3645 (3 x+2)^5}-\frac{200}{729} \log (3 x+2) \]

[Out]

-343/(3645*(2 + 3*x)^5) + 931/(729*(2 + 3*x)^4) - 11599/(2187*(2 + 3*x)^3) + 409
9/(729*(2 + 3*x)^2) - 2180/(729*(2 + 3*x)) - (200*Log[2 + 3*x])/729

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Rubi [A]  time = 0.0635281, antiderivative size = 66, 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 \[ -\frac{2180}{729 (3 x+2)}+\frac{4099}{729 (3 x+2)^2}-\frac{11599}{2187 (3 x+2)^3}+\frac{931}{729 (3 x+2)^4}-\frac{343}{3645 (3 x+2)^5}-\frac{200}{729} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^6,x]

[Out]

-343/(3645*(2 + 3*x)^5) + 931/(729*(2 + 3*x)^4) - 11599/(2187*(2 + 3*x)^3) + 409
9/(729*(2 + 3*x)^2) - 2180/(729*(2 + 3*x)) - (200*Log[2 + 3*x])/729

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Rubi in Sympy [A]  time = 10.5352, size = 56, normalized size = 0.85 \[ - \frac{200 \log{\left (3 x + 2 \right )}}{729} - \frac{2180}{729 \left (3 x + 2\right )} + \frac{4099}{729 \left (3 x + 2\right )^{2}} - \frac{11599}{2187 \left (3 x + 2\right )^{3}} + \frac{931}{729 \left (3 x + 2\right )^{4}} - \frac{343}{3645 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**6,x)

[Out]

-200*log(3*x + 2)/729 - 2180/(729*(3*x + 2)) + 4099/(729*(3*x + 2)**2) - 11599/(
2187*(3*x + 2)**3) + 931/(729*(3*x + 2)**4) - 343/(3645*(3*x + 2)**5)

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Mathematica [A]  time = 0.0560005, size = 46, normalized size = 0.7 \[ -\frac{2648700 x^4+5403105 x^3+4264965 x^2+1579785 x+3000 (3 x+2)^5 \log (30 x+20)+236399}{10935 (3 x+2)^5} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^6,x]

[Out]

-(236399 + 1579785*x + 4264965*x^2 + 5403105*x^3 + 2648700*x^4 + 3000*(2 + 3*x)^
5*Log[20 + 30*x])/(10935*(2 + 3*x)^5)

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Maple [A]  time = 0.012, size = 55, normalized size = 0.8 \[ -{\frac{343}{3645\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{931}{729\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{11599}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{4099}{729\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{2180}{1458+2187\,x}}-{\frac{200\,\ln \left ( 2+3\,x \right ) }{729}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(3+5*x)^2/(2+3*x)^6,x)

[Out]

-343/3645/(2+3*x)^5+931/729/(2+3*x)^4-11599/2187/(2+3*x)^3+4099/729/(2+3*x)^2-21
80/729/(2+3*x)-200/729*ln(2+3*x)

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Maxima [A]  time = 1.33377, size = 78, normalized size = 1.18 \[ -\frac{2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 1579785 \, x + 236399}{10935 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} - \frac{200}{729} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="maxima")

[Out]

-1/10935*(2648700*x^4 + 5403105*x^3 + 4264965*x^2 + 1579785*x + 236399)/(243*x^5
+ 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32) - 200/729*log(3*x + 2)

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Fricas [A]  time = 0.213722, size = 111, normalized size = 1.68 \[ -\frac{2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 3000 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 1579785 \, x + 236399}{10935 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="fricas")

[Out]

-1/10935*(2648700*x^4 + 5403105*x^3 + 4264965*x^2 + 3000*(243*x^5 + 810*x^4 + 10
80*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 1579785*x + 236399)/(243*x^5 + 810
*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)

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Sympy [A]  time = 0.427891, size = 56, normalized size = 0.85 \[ - \frac{2648700 x^{4} + 5403105 x^{3} + 4264965 x^{2} + 1579785 x + 236399}{2657205 x^{5} + 8857350 x^{4} + 11809800 x^{3} + 7873200 x^{2} + 2624400 x + 349920} - \frac{200 \log{\left (3 x + 2 \right )}}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**6,x)

[Out]

-(2648700*x**4 + 5403105*x**3 + 4264965*x**2 + 1579785*x + 236399)/(2657205*x**5
+ 8857350*x**4 + 11809800*x**3 + 7873200*x**2 + 2624400*x + 349920) - 200*log(3
*x + 2)/729

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GIAC/XCAS [A]  time = 0.20718, size = 53, normalized size = 0.8 \[ -\frac{2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 1579785 \, x + 236399}{10935 \,{\left (3 \, x + 2\right )}^{5}} - \frac{200}{729} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^6,x, algorithm="giac")

[Out]

-1/10935*(2648700*x^4 + 5403105*x^3 + 4264965*x^2 + 1579785*x + 236399)/(3*x + 2
)^5 - 200/729*ln(abs(3*x + 2))