3.1172 \(\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^6} \, dx\)

Optimal. Leaf size=37 \[ \frac{5 (5 x+3)^4}{12 (3 x+2)^4}+\frac{7 (5 x+3)^4}{15 (3 x+2)^5} \]

[Out]

(7*(3 + 5*x)^4)/(15*(2 + 3*x)^5) + (5*(3 + 5*x)^4)/(12*(2 + 3*x)^4)

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Rubi [A]  time = 0.036063, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{5 (5 x+3)^4}{12 (3 x+2)^4}+\frac{7 (5 x+3)^4}{15 (3 x+2)^5} \]

Antiderivative was successfully verified.

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

[Out]

(7*(3 + 5*x)^4)/(15*(2 + 3*x)^5) + (5*(3 + 5*x)^4)/(12*(2 + 3*x)^4)

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Rubi in Sympy [A]  time = 5.35374, size = 32, normalized size = 0.86 \[ \frac{5 \left (5 x + 3\right )^{4}}{12 \left (3 x + 2\right )^{4}} + \frac{7 \left (5 x + 3\right )^{4}}{15 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*(5*x + 3)**4/(12*(3*x + 2)**4) + 7*(5*x + 3)**4/(15*(3*x + 2)**5)

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Mathematica [A]  time = 0.0157371, size = 31, normalized size = 0.84 \[ \frac{405000 x^4+803250 x^3+559800 x^2+153795 x+11758}{4860 (3 x+2)^5} \]

Antiderivative was successfully verified.

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

[Out]

(11758 + 153795*x + 559800*x^2 + 803250*x^3 + 405000*x^4)/(4860*(2 + 3*x)^5)

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Maple [A]  time = 0.009, size = 47, normalized size = 1.3 \[{\frac{7}{1215\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{250}{486+729\,x}}+{\frac{185}{243\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{107}{972\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{1025}{486\, \left ( 2+3\,x \right ) ^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7/1215/(2+3*x)^5+250/243/(2+3*x)+185/243/(2+3*x)^3-107/972/(2+3*x)^4-1025/486/(2
+3*x)^2

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Maxima [A]  time = 1.35347, size = 66, normalized size = 1.78 \[ \frac{405000 \, x^{4} + 803250 \, x^{3} + 559800 \, x^{2} + 153795 \, x + 11758}{4860 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4860*(405000*x^4 + 803250*x^3 + 559800*x^2 + 153795*x + 11758)/(243*x^5 + 810*
x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)

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Fricas [A]  time = 0.208874, size = 66, normalized size = 1.78 \[ \frac{405000 \, x^{4} + 803250 \, x^{3} + 559800 \, x^{2} + 153795 \, x + 11758}{4860 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4860*(405000*x^4 + 803250*x^3 + 559800*x^2 + 153795*x + 11758)/(243*x^5 + 810*
x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)

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Sympy [A]  time = 0.412406, size = 44, normalized size = 1.19 \[ \frac{405000 x^{4} + 803250 x^{3} + 559800 x^{2} + 153795 x + 11758}{1180980 x^{5} + 3936600 x^{4} + 5248800 x^{3} + 3499200 x^{2} + 1166400 x + 155520} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(405000*x**4 + 803250*x**3 + 559800*x**2 + 153795*x + 11758)/(1180980*x**5 + 393
6600*x**4 + 5248800*x**3 + 3499200*x**2 + 1166400*x + 155520)

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GIAC/XCAS [A]  time = 0.208729, size = 39, normalized size = 1.05 \[ \frac{405000 \, x^{4} + 803250 \, x^{3} + 559800 \, x^{2} + 153795 \, x + 11758}{4860 \,{\left (3 \, x + 2\right )}^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4860*(405000*x^4 + 803250*x^3 + 559800*x^2 + 153795*x + 11758)/(3*x + 2)^5