3.1157 \(\int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=45 \[ \frac{25}{162 (3 x+2)^4}-\frac{13}{27 (3 x+2)^5}+\frac{4}{27 (3 x+2)^6}-\frac{1}{81 (3 x+2)^7} \]

[Out]

-1/(81*(2 + 3*x)^7) + 4/(27*(2 + 3*x)^6) - 13/(27*(2 + 3*x)^5) + 25/(162*(2 + 3*
x)^4)

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Rubi [A]  time = 0.0506092, 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 \[ \frac{25}{162 (3 x+2)^4}-\frac{13}{27 (3 x+2)^5}+\frac{4}{27 (3 x+2)^6}-\frac{1}{81 (3 x+2)^7} \]

Antiderivative was successfully verified.

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

[Out]

-1/(81*(2 + 3*x)^7) + 4/(27*(2 + 3*x)^6) - 13/(27*(2 + 3*x)^5) + 25/(162*(2 + 3*
x)^4)

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Rubi in Sympy [A]  time = 8.31563, size = 39, normalized size = 0.87 \[ \frac{25}{162 \left (3 x + 2\right )^{4}} - \frac{13}{27 \left (3 x + 2\right )^{5}} + \frac{4}{27 \left (3 x + 2\right )^{6}} - \frac{1}{81 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/(162*(3*x + 2)**4) - 13/(27*(3*x + 2)**5) + 4/(27*(3*x + 2)**6) - 1/(81*(3*x
+ 2)**7)

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Mathematica [A]  time = 0.0138981, size = 26, normalized size = 0.58 \[ \frac{225 x^3+216 x^2+12 x-22}{54 (3 x+2)^7} \]

Antiderivative was successfully verified.

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

[Out]

(-22 + 12*x + 216*x^2 + 225*x^3)/(54*(2 + 3*x)^7)

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Maple [A]  time = 0.007, size = 38, normalized size = 0.8 \[ -{\frac{1}{81\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{4}{27\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{13}{27\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{25}{162\, \left ( 2+3\,x \right ) ^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/81/(2+3*x)^7+4/27/(2+3*x)^6-13/27/(2+3*x)^5+25/162/(2+3*x)^4

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Maxima [A]  time = 1.34298, size = 73, normalized size = 1.62 \[ \frac{225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/54*(225*x^3 + 216*x^2 + 12*x - 22)/(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 = 0.205392, size = 73, normalized size = 1.62 \[ \frac{225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/54*(225*x^3 + 216*x^2 + 12*x - 22)/(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 = 0.443811, size = 49, normalized size = 1.09 \[ \frac{225 x^{3} + 216 x^{2} + 12 x - 22}{118098 x^{7} + 551124 x^{6} + 1102248 x^{5} + 1224720 x^{4} + 816480 x^{3} + 326592 x^{2} + 72576 x + 6912} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(225*x**3 + 216*x**2 + 12*x - 22)/(118098*x**7 + 551124*x**6 + 1102248*x**5 + 12
24720*x**4 + 816480*x**3 + 326592*x**2 + 72576*x + 6912)

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GIAC/XCAS [A]  time = 0.210531, size = 32, normalized size = 0.71 \[ \frac{225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \,{\left (3 \, x + 2\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/54*(225*x^3 + 216*x^2 + 12*x - 22)/(3*x + 2)^7