3.1337 \(\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=56 \[ \frac{40}{729 (3 x+2)^3}-\frac{107}{243 (3 x+2)^4}+\frac{518}{405 (3 x+2)^5}-\frac{2009}{1458 (3 x+2)^6}+\frac{49}{243 (3 x+2)^7} \]

[Out]

49/(243*(2 + 3*x)^7) - 2009/(1458*(2 + 3*x)^6) + 518/(405*(2 + 3*x)^5) - 107/(24
3*(2 + 3*x)^4) + 40/(729*(2 + 3*x)^3)

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Rubi [A]  time = 0.0589569, antiderivative size = 56, 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 \[ \frac{40}{729 (3 x+2)^3}-\frac{107}{243 (3 x+2)^4}+\frac{518}{405 (3 x+2)^5}-\frac{2009}{1458 (3 x+2)^6}+\frac{49}{243 (3 x+2)^7} \]

Antiderivative was successfully verified.

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

[Out]

49/(243*(2 + 3*x)^7) - 2009/(1458*(2 + 3*x)^6) + 518/(405*(2 + 3*x)^5) - 107/(24
3*(2 + 3*x)^4) + 40/(729*(2 + 3*x)^3)

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Rubi in Sympy [A]  time = 9.66135, size = 49, normalized size = 0.88 \[ \frac{40}{729 \left (3 x + 2\right )^{3}} - \frac{107}{243 \left (3 x + 2\right )^{4}} + \frac{518}{405 \left (3 x + 2\right )^{5}} - \frac{2009}{1458 \left (3 x + 2\right )^{6}} + \frac{49}{243 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

40/(729*(3*x + 2)**3) - 107/(243*(3*x + 2)**4) + 518/(405*(3*x + 2)**5) - 2009/(
1458*(3*x + 2)**6) + 49/(243*(3*x + 2)**7)

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Mathematica [A]  time = 0.0180323, size = 31, normalized size = 0.55 \[ \frac{32400 x^4-270 x^3-3024 x^2+4593 x-604}{7290 (3 x+2)^7} \]

Antiderivative was successfully verified.

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

[Out]

(-604 + 4593*x - 3024*x^2 - 270*x^3 + 32400*x^4)/(7290*(2 + 3*x)^7)

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Maple [A]  time = 0.01, size = 47, normalized size = 0.8 \[{\frac{49}{243\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{2009}{1458\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{518}{405\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{107}{243\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{40}{729\, \left ( 2+3\,x \right ) ^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/243/(2+3*x)^7-2009/1458/(2+3*x)^6+518/405/(2+3*x)^5-107/243/(2+3*x)^4+40/729/
(2+3*x)^3

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Maxima [A]  time = 1.34744, size = 80, normalized size = 1.43 \[ \frac{32400 \, x^{4} - 270 \, x^{3} - 3024 \, x^{2} + 4593 \, x - 604}{7290 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7290*(32400*x^4 - 270*x^3 - 3024*x^2 + 4593*x - 604)/(2187*x^7 + 10206*x^6 + 2
0412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

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Fricas [A]  time = 0.219667, size = 80, normalized size = 1.43 \[ \frac{32400 \, x^{4} - 270 \, x^{3} - 3024 \, x^{2} + 4593 \, x - 604}{7290 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7290*(32400*x^4 - 270*x^3 - 3024*x^2 + 4593*x - 604)/(2187*x^7 + 10206*x^6 + 2
0412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

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Sympy [A]  time = 0.471707, size = 54, normalized size = 0.96 \[ \frac{32400 x^{4} - 270 x^{3} - 3024 x^{2} + 4593 x - 604}{15943230 x^{7} + 74401740 x^{6} + 148803480 x^{5} + 165337200 x^{4} + 110224800 x^{3} + 44089920 x^{2} + 9797760 x + 933120} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(32400*x**4 - 270*x**3 - 3024*x**2 + 4593*x - 604)/(15943230*x**7 + 74401740*x**
6 + 148803480*x**5 + 165337200*x**4 + 110224800*x**3 + 44089920*x**2 + 9797760*x
+ 933120)

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GIAC/XCAS [A]  time = 0.203325, size = 39, normalized size = 0.7 \[ \frac{32400 \, x^{4} - 270 \, x^{3} - 3024 \, x^{2} + 4593 \, x - 604}{7290 \,{\left (3 \, x + 2\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7290*(32400*x^4 - 270*x^3 - 3024*x^2 + 4593*x - 604)/(3*x + 2)^7