3.1354 \(\int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=67 \[ \frac{100}{729 (3 x+2)^2}-\frac{2180}{2187 (3 x+2)^3}+\frac{4099}{1458 (3 x+2)^4}-\frac{11599}{3645 (3 x+2)^5}+\frac{1862}{2187 (3 x+2)^6}-\frac{49}{729 (3 x+2)^7} \]

[Out]

-49/(729*(2 + 3*x)^7) + 1862/(2187*(2 + 3*x)^6) - 11599/(3645*(2 + 3*x)^5) + 409
9/(1458*(2 + 3*x)^4) - 2180/(2187*(2 + 3*x)^3) + 100/(729*(2 + 3*x)^2)

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Rubi [A]  time = 0.0716052, antiderivative size = 67, 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 \[ \frac{100}{729 (3 x+2)^2}-\frac{2180}{2187 (3 x+2)^3}+\frac{4099}{1458 (3 x+2)^4}-\frac{11599}{3645 (3 x+2)^5}+\frac{1862}{2187 (3 x+2)^6}-\frac{49}{729 (3 x+2)^7} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^8,x]

[Out]

-49/(729*(2 + 3*x)^7) + 1862/(2187*(2 + 3*x)^6) - 11599/(3645*(2 + 3*x)^5) + 409
9/(1458*(2 + 3*x)^4) - 2180/(2187*(2 + 3*x)^3) + 100/(729*(2 + 3*x)^2)

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Rubi in Sympy [A]  time = 11.5506, size = 60, normalized size = 0.9 \[ \frac{100}{729 \left (3 x + 2\right )^{2}} - \frac{2180}{2187 \left (3 x + 2\right )^{3}} + \frac{4099}{1458 \left (3 x + 2\right )^{4}} - \frac{11599}{3645 \left (3 x + 2\right )^{5}} + \frac{1862}{2187 \left (3 x + 2\right )^{6}} - \frac{49}{729 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**8,x)

[Out]

100/(729*(3*x + 2)**2) - 2180/(2187*(3*x + 2)**3) + 4099/(1458*(3*x + 2)**4) - 1
1599/(3645*(3*x + 2)**5) + 1862/(2187*(3*x + 2)**6) - 49/(729*(3*x + 2)**7)

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Mathematica [A]  time = 0.0412548, size = 36, normalized size = 0.54 \[ \frac{729000 x^5+664200 x^4+191295 x^3+145044 x^2+61392 x-3526}{21870 (3 x+2)^7} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^8,x]

[Out]

(-3526 + 61392*x + 145044*x^2 + 191295*x^3 + 664200*x^4 + 729000*x^5)/(21870*(2
+ 3*x)^7)

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Maple [A]  time = 0.01, size = 56, normalized size = 0.8 \[ -{\frac{49}{729\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{1862}{2187\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{11599}{3645\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{4099}{1458\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{2180}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{100}{729\, \left ( 2+3\,x \right ) ^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(3+5*x)^2/(2+3*x)^8,x)

[Out]

-49/729/(2+3*x)^7+1862/2187/(2+3*x)^6-11599/3645/(2+3*x)^5+4099/1458/(2+3*x)^4-2
180/2187/(2+3*x)^3+100/729/(2+3*x)^2

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Maxima [A]  time = 1.34967, size = 86, normalized size = 1.28 \[ \frac{729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^8,x, algorithm="maxima")

[Out]

1/21870*(729000*x^5 + 664200*x^4 + 191295*x^3 + 145044*x^2 + 61392*x - 3526)/(21
87*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128
)

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Fricas [A]  time = 0.19475, size = 86, normalized size = 1.28 \[ \frac{729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^8,x, algorithm="fricas")

[Out]

1/21870*(729000*x^5 + 664200*x^4 + 191295*x^3 + 145044*x^2 + 61392*x - 3526)/(21
87*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128
)

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Sympy [A]  time = 0.526282, size = 60, normalized size = 0.9 \[ \frac{729000 x^{5} + 664200 x^{4} + 191295 x^{3} + 145044 x^{2} + 61392 x - 3526}{47829690 x^{7} + 223205220 x^{6} + 446410440 x^{5} + 496011600 x^{4} + 330674400 x^{3} + 132269760 x^{2} + 29393280 x + 2799360} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**8,x)

[Out]

(729000*x**5 + 664200*x**4 + 191295*x**3 + 145044*x**2 + 61392*x - 3526)/(478296
90*x**7 + 223205220*x**6 + 446410440*x**5 + 496011600*x**4 + 330674400*x**3 + 13
2269760*x**2 + 29393280*x + 2799360)

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GIAC/XCAS [A]  time = 0.210854, size = 46, normalized size = 0.69 \[ \frac{729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \,{\left (3 \, x + 2\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^8,x, algorithm="giac")

[Out]

1/21870*(729000*x^5 + 664200*x^4 + 191295*x^3 + 145044*x^2 + 61392*x - 3526)/(3*
x + 2)^7