3.1336 \(\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^7} \, dx\)

Optimal. Leaf size=55 \[ -\frac{103 (1-2 x)^4}{30870 (3 x+2)^4}-\frac{103 (1-2 x)^4}{2205 (3 x+2)^5}+\frac{(1-2 x)^4}{126 (3 x+2)^6} \]

[Out]

(1 - 2*x)^4/(126*(2 + 3*x)^6) - (103*(1 - 2*x)^4)/(2205*(2 + 3*x)^5) - (103*(1 -
2*x)^4)/(30870*(2 + 3*x)^4)

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Rubi [A]  time = 0.0511621, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ -\frac{103 (1-2 x)^4}{30870 (3 x+2)^4}-\frac{103 (1-2 x)^4}{2205 (3 x+2)^5}+\frac{(1-2 x)^4}{126 (3 x+2)^6} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^7,x]

[Out]

(1 - 2*x)^4/(126*(2 + 3*x)^6) - (103*(1 - 2*x)^4)/(2205*(2 + 3*x)^5) - (103*(1 -
2*x)^4)/(30870*(2 + 3*x)^4)

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Rubi in Sympy [A]  time = 6.90601, size = 48, normalized size = 0.87 \[ - \frac{103 \left (- 2 x + 1\right )^{4}}{30870 \left (3 x + 2\right )^{4}} - \frac{103 \left (- 2 x + 1\right )^{4}}{2205 \left (3 x + 2\right )^{5}} + \frac{\left (- 2 x + 1\right )^{4}}{126 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(3+5*x)/(2+3*x)**7,x)

[Out]

-103*(-2*x + 1)**4/(30870*(3*x + 2)**4) - 103*(-2*x + 1)**4/(2205*(3*x + 2)**5)
+ (-2*x + 1)**4/(126*(3*x + 2)**6)

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Mathematica [A]  time = 0.0166663, size = 31, normalized size = 0.56 \[ \frac{48600 x^4+14040 x^3+3375 x^2+7218 x-413}{7290 (3 x+2)^6} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^7,x]

[Out]

(-413 + 7218*x + 3375*x^2 + 14040*x^3 + 48600*x^4)/(7290*(2 + 3*x)^6)

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Maple [A]  time = 0.009, size = 47, normalized size = 0.9 \[ -{\frac{2009}{1215\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{428}{729\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{259}{162\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{20}{243\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{343}{1458\, \left ( 2+3\,x \right ) ^{6}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(3+5*x)/(2+3*x)^7,x)

[Out]

-2009/1215/(2+3*x)^5-428/729/(2+3*x)^3+259/162/(2+3*x)^4+20/243/(2+3*x)^2+343/14
58/(2+3*x)^6

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Maxima [A]  time = 1.34553, size = 73, normalized size = 1.33 \[ \frac{48600 \, x^{4} + 14040 \, x^{3} + 3375 \, x^{2} + 7218 \, x - 413}{7290 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^7,x, algorithm="maxima")

[Out]

1/7290*(48600*x^4 + 14040*x^3 + 3375*x^2 + 7218*x - 413)/(729*x^6 + 2916*x^5 + 4
860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)

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Fricas [A]  time = 0.20242, size = 73, normalized size = 1.33 \[ \frac{48600 \, x^{4} + 14040 \, x^{3} + 3375 \, x^{2} + 7218 \, x - 413}{7290 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^7,x, algorithm="fricas")

[Out]

1/7290*(48600*x^4 + 14040*x^3 + 3375*x^2 + 7218*x - 413)/(729*x^6 + 2916*x^5 + 4
860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)

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Sympy [A]  time = 0.42432, size = 49, normalized size = 0.89 \[ \frac{48600 x^{4} + 14040 x^{3} + 3375 x^{2} + 7218 x - 413}{5314410 x^{6} + 21257640 x^{5} + 35429400 x^{4} + 31492800 x^{3} + 15746400 x^{2} + 4199040 x + 466560} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(3+5*x)/(2+3*x)**7,x)

[Out]

(48600*x**4 + 14040*x**3 + 3375*x**2 + 7218*x - 413)/(5314410*x**6 + 21257640*x*
*5 + 35429400*x**4 + 31492800*x**3 + 15746400*x**2 + 4199040*x + 466560)

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GIAC/XCAS [A]  time = 0.209535, size = 39, normalized size = 0.71 \[ \frac{48600 \, x^{4} + 14040 \, x^{3} + 3375 \, x^{2} + 7218 \, x - 413}{7290 \,{\left (3 \, x + 2\right )}^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^7,x, algorithm="giac")

[Out]

1/7290*(48600*x^4 + 14040*x^3 + 3375*x^2 + 7218*x - 413)/(3*x + 2)^6