3.1233 \(\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx\)

Optimal. Leaf size=45 \[ -\frac{10}{81 (3 x+2)^2}+\frac{16}{27 (3 x+2)^3}-\frac{91}{108 (3 x+2)^4}+\frac{49}{405 (3 x+2)^5} \]

[Out]

49/(405*(2 + 3*x)^5) - 91/(108*(2 + 3*x)^4) + 16/(27*(2 + 3*x)^3) - 10/(81*(2 +
3*x)^2)

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Rubi [A]  time = 0.0502313, 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 \[ -\frac{10}{81 (3 x+2)^2}+\frac{16}{27 (3 x+2)^3}-\frac{91}{108 (3 x+2)^4}+\frac{49}{405 (3 x+2)^5} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^6,x]

[Out]

49/(405*(2 + 3*x)^5) - 91/(108*(2 + 3*x)^4) + 16/(27*(2 + 3*x)^3) - 10/(81*(2 +
3*x)^2)

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Rubi in Sympy [A]  time = 8.11236, size = 39, normalized size = 0.87 \[ - \frac{10}{81 \left (3 x + 2\right )^{2}} + \frac{16}{27 \left (3 x + 2\right )^{3}} - \frac{91}{108 \left (3 x + 2\right )^{4}} + \frac{49}{405 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(3+5*x)/(2+3*x)**6,x)

[Out]

-10/(81*(3*x + 2)**2) + 16/(27*(3*x + 2)**3) - 91/(108*(3*x + 2)**4) + 49/(405*(
3*x + 2)**5)

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Mathematica [A]  time = 0.0178947, size = 26, normalized size = 0.58 \[ -\frac{1800 x^3+720 x^2-75 x+98}{540 (3 x+2)^5} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^6,x]

[Out]

-(98 - 75*x + 720*x^2 + 1800*x^3)/(540*(2 + 3*x)^5)

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Maple [A]  time = 0.009, size = 38, normalized size = 0.8 \[{\frac{49}{405\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{91}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{16}{27\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{10}{81\, \left ( 2+3\,x \right ) ^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(3+5*x)/(2+3*x)^6,x)

[Out]

49/405/(2+3*x)^5-91/108/(2+3*x)^4+16/27/(2+3*x)^3-10/81/(2+3*x)^2

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Maxima [A]  time = 1.34741, size = 59, normalized size = 1.31 \[ -\frac{1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^6,x, algorithm="maxima")

[Out]

-1/540*(1800*x^3 + 720*x^2 - 75*x + 98)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2
+ 240*x + 32)

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Fricas [A]  time = 0.19445, size = 59, normalized size = 1.31 \[ -\frac{1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^6,x, algorithm="fricas")

[Out]

-1/540*(1800*x^3 + 720*x^2 - 75*x + 98)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2
+ 240*x + 32)

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Sympy [A]  time = 0.373676, size = 41, normalized size = 0.91 \[ - \frac{1800 x^{3} + 720 x^{2} - 75 x + 98}{131220 x^{5} + 437400 x^{4} + 583200 x^{3} + 388800 x^{2} + 129600 x + 17280} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(3+5*x)/(2+3*x)**6,x)

[Out]

-(1800*x**3 + 720*x**2 - 75*x + 98)/(131220*x**5 + 437400*x**4 + 583200*x**3 + 3
88800*x**2 + 129600*x + 17280)

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GIAC/XCAS [A]  time = 0.207269, size = 32, normalized size = 0.71 \[ -\frac{1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \,{\left (3 \, x + 2\right )}^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^6,x, algorithm="giac")

[Out]

-1/540*(1800*x^3 + 720*x^2 - 75*x + 98)/(3*x + 2)^5