3.1235 \(\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=45 \[ -\frac{5}{81 (3 x+2)^4}+\frac{16}{45 (3 x+2)^5}-\frac{91}{162 (3 x+2)^6}+\frac{7}{81 (3 x+2)^7} \]

[Out]

7/(81*(2 + 3*x)^7) - 91/(162*(2 + 3*x)^6) + 16/(45*(2 + 3*x)^5) - 5/(81*(2 + 3*x
)^4)

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Rubi [A]  time = 0.0508431, antiderivative size = 45, 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 \[ -\frac{5}{81 (3 x+2)^4}+\frac{16}{45 (3 x+2)^5}-\frac{91}{162 (3 x+2)^6}+\frac{7}{81 (3 x+2)^7} \]

Antiderivative was successfully verified.

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

[Out]

7/(81*(2 + 3*x)^7) - 91/(162*(2 + 3*x)^6) + 16/(45*(2 + 3*x)^5) - 5/(81*(2 + 3*x
)^4)

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Rubi in Sympy [A]  time = 8.24041, size = 39, normalized size = 0.87 \[ - \frac{5}{81 \left (3 x + 2\right )^{4}} + \frac{16}{45 \left (3 x + 2\right )^{5}} - \frac{91}{162 \left (3 x + 2\right )^{6}} + \frac{7}{81 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/(81*(3*x + 2)**4) + 16/(45*(3*x + 2)**5) - 91/(162*(3*x + 2)**6) + 7/(81*(3*x
+ 2)**7)

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Mathematica [A]  time = 0.0176707, size = 26, normalized size = 0.58 \[ -\frac{1350 x^3+108 x^2-291 x+88}{810 (3 x+2)^7} \]

Antiderivative was successfully verified.

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

[Out]

-(88 - 291*x + 108*x^2 + 1350*x^3)/(810*(2 + 3*x)^7)

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Maple [A]  time = 0.009, size = 38, normalized size = 0.8 \[{\frac{7}{81\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{91}{162\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{16}{45\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{5}{81\, \left ( 2+3\,x \right ) ^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7/81/(2+3*x)^7-91/162/(2+3*x)^6+16/45/(2+3*x)^5-5/81/(2+3*x)^4

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Maxima [A]  time = 1.35002, size = 73, normalized size = 1.62 \[ -\frac{1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/810*(1350*x^3 + 108*x^2 - 291*x + 88)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 226
80*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

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Fricas [A]  time = 0.202764, size = 73, normalized size = 1.62 \[ -\frac{1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/810*(1350*x^3 + 108*x^2 - 291*x + 88)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 226
80*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

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Sympy [A]  time = 0.450358, size = 51, normalized size = 1.13 \[ - \frac{1350 x^{3} + 108 x^{2} - 291 x + 88}{1771470 x^{7} + 8266860 x^{6} + 16533720 x^{5} + 18370800 x^{4} + 12247200 x^{3} + 4898880 x^{2} + 1088640 x + 103680} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1350*x**3 + 108*x**2 - 291*x + 88)/(1771470*x**7 + 8266860*x**6 + 16533720*x**
5 + 18370800*x**4 + 12247200*x**3 + 4898880*x**2 + 1088640*x + 103680)

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GIAC/XCAS [A]  time = 0.207325, size = 32, normalized size = 0.71 \[ -\frac{1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \,{\left (3 \, x + 2\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/810*(1350*x^3 + 108*x^2 - 291*x + 88)/(3*x + 2)^7