3.1370 \(\int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=78 \[ \frac{1000}{2187 (3 x+2)}-\frac{1850}{729 (3 x+2)^2}+\frac{14390}{2187 (3 x+2)^3}-\frac{66193}{8748 (3 x+2)^4}+\frac{10073}{3645 (3 x+2)^5}-\frac{1813}{4374 (3 x+2)^6}+\frac{49}{2187 (3 x+2)^7} \]

[Out]

49/(2187*(2 + 3*x)^7) - 1813/(4374*(2 + 3*x)^6) + 10073/(3645*(2 + 3*x)^5) - 661
93/(8748*(2 + 3*x)^4) + 14390/(2187*(2 + 3*x)^3) - 1850/(729*(2 + 3*x)^2) + 1000
/(2187*(2 + 3*x))

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Rubi [A]  time = 0.0819502, antiderivative size = 78, 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 \[ \frac{1000}{2187 (3 x+2)}-\frac{1850}{729 (3 x+2)^2}+\frac{14390}{2187 (3 x+2)^3}-\frac{66193}{8748 (3 x+2)^4}+\frac{10073}{3645 (3 x+2)^5}-\frac{1813}{4374 (3 x+2)^6}+\frac{49}{2187 (3 x+2)^7} \]

Antiderivative was successfully verified.

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

[Out]

49/(2187*(2 + 3*x)^7) - 1813/(4374*(2 + 3*x)^6) + 10073/(3645*(2 + 3*x)^5) - 661
93/(8748*(2 + 3*x)^4) + 14390/(2187*(2 + 3*x)^3) - 1850/(729*(2 + 3*x)^2) + 1000
/(2187*(2 + 3*x))

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Rubi in Sympy [A]  time = 13.207, size = 66, normalized size = 0.85 \[ \frac{1000}{2187 \left (3 x + 2\right )} - \frac{1850}{729 \left (3 x + 2\right )^{2}} + \frac{14390}{2187 \left (3 x + 2\right )^{3}} - \frac{66193}{8748 \left (3 x + 2\right )^{4}} + \frac{10073}{3645 \left (3 x + 2\right )^{5}} - \frac{1813}{4374 \left (3 x + 2\right )^{6}} + \frac{49}{2187 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1000/(2187*(3*x + 2)) - 1850/(729*(3*x + 2)**2) + 14390/(2187*(3*x + 2)**3) - 66
193/(8748*(3*x + 2)**4) + 10073/(3645*(3*x + 2)**5) - 1813/(4374*(3*x + 2)**6) +
49/(2187*(3*x + 2)**7)

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Mathematica [A]  time = 0.0215397, size = 41, normalized size = 0.53 \[ \frac{14580000 x^6+31347000 x^5+30601800 x^4+19748745 x^3+8660574 x^2+1990182 x+133304}{43740 (3 x+2)^7} \]

Antiderivative was successfully verified.

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

[Out]

(133304 + 1990182*x + 8660574*x^2 + 19748745*x^3 + 30601800*x^4 + 31347000*x^5 +
14580000*x^6)/(43740*(2 + 3*x)^7)

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Maple [A]  time = 0.008, size = 65, normalized size = 0.8 \[{\frac{49}{2187\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{1813}{4374\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{10073}{3645\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{66193}{8748\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{14390}{2187\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1850}{729\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{1000}{4374+6561\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/2187/(2+3*x)^7-1813/4374/(2+3*x)^6+10073/3645/(2+3*x)^5-66193/8748/(2+3*x)^4+
14390/2187/(2+3*x)^3-1850/729/(2+3*x)^2+1000/2187/(2+3*x)

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Maxima [A]  time = 1.3491, size = 93, normalized size = 1.19 \[ \frac{14580000 \, x^{6} + 31347000 \, x^{5} + 30601800 \, x^{4} + 19748745 \, x^{3} + 8660574 \, x^{2} + 1990182 \, x + 133304}{43740 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/43740*(14580000*x^6 + 31347000*x^5 + 30601800*x^4 + 19748745*x^3 + 8660574*x^2
+ 1990182*x + 133304)/(2187*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 = 0.205223, size = 93, normalized size = 1.19 \[ \frac{14580000 \, x^{6} + 31347000 \, x^{5} + 30601800 \, x^{4} + 19748745 \, x^{3} + 8660574 \, x^{2} + 1990182 \, x + 133304}{43740 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/43740*(14580000*x^6 + 31347000*x^5 + 30601800*x^4 + 19748745*x^3 + 8660574*x^2
+ 1990182*x + 133304)/(2187*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 = 0.511404, size = 65, normalized size = 0.83 \[ \frac{14580000 x^{6} + 31347000 x^{5} + 30601800 x^{4} + 19748745 x^{3} + 8660574 x^{2} + 1990182 x + 133304}{95659380 x^{7} + 446410440 x^{6} + 892820880 x^{5} + 992023200 x^{4} + 661348800 x^{3} + 264539520 x^{2} + 58786560 x + 5598720} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(14580000*x**6 + 31347000*x**5 + 30601800*x**4 + 19748745*x**3 + 8660574*x**2 +
1990182*x + 133304)/(95659380*x**7 + 446410440*x**6 + 892820880*x**5 + 992023200
*x**4 + 661348800*x**3 + 264539520*x**2 + 58786560*x + 5598720)

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GIAC/XCAS [A]  time = 0.213977, size = 53, normalized size = 0.68 \[ \frac{14580000 \, x^{6} + 31347000 \, x^{5} + 30601800 \, x^{4} + 19748745 \, x^{3} + 8660574 \, x^{2} + 1990182 \, x + 133304}{43740 \,{\left (3 \, x + 2\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/43740*(14580000*x^6 + 31347000*x^5 + 30601800*x^4 + 19748745*x^3 + 8660574*x^2
+ 1990182*x + 133304)/(3*x + 2)^7