3.2120 \(\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^{5/2}} \, dx\)

Optimal. Leaf size=66 \[ -\frac{27}{16} (1-2 x)^{5/2}+\frac{207}{8} (1-2 x)^{3/2}-\frac{1071}{4} \sqrt{1-2 x}-\frac{3283}{8 \sqrt{1-2 x}}+\frac{3773}{48 (1-2 x)^{3/2}} \]

[Out]

3773/(48*(1 - 2*x)^(3/2)) - 3283/(8*Sqrt[1 - 2*x]) - (1071*Sqrt[1 - 2*x])/4 + (2
07*(1 - 2*x)^(3/2))/8 - (27*(1 - 2*x)^(5/2))/16

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Rubi [A]  time = 0.0551939, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{27}{16} (1-2 x)^{5/2}+\frac{207}{8} (1-2 x)^{3/2}-\frac{1071}{4} \sqrt{1-2 x}-\frac{3283}{8 \sqrt{1-2 x}}+\frac{3773}{48 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

3773/(48*(1 - 2*x)^(3/2)) - 3283/(8*Sqrt[1 - 2*x]) - (1071*Sqrt[1 - 2*x])/4 + (2
07*(1 - 2*x)^(3/2))/8 - (27*(1 - 2*x)^(5/2))/16

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Rubi in Sympy [A]  time = 7.95968, size = 58, normalized size = 0.88 \[ - \frac{27 \left (- 2 x + 1\right )^{\frac{5}{2}}}{16} + \frac{207 \left (- 2 x + 1\right )^{\frac{3}{2}}}{8} - \frac{1071 \sqrt{- 2 x + 1}}{4} - \frac{3283}{8 \sqrt{- 2 x + 1}} + \frac{3773}{48 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27*(-2*x + 1)**(5/2)/16 + 207*(-2*x + 1)**(3/2)/8 - 1071*sqrt(-2*x + 1)/4 - 328
3/(8*sqrt(-2*x + 1)) + 3773/(48*(-2*x + 1)**(3/2))

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Mathematica [A]  time = 0.0459921, size = 33, normalized size = 0.5 \[ -\frac{81 x^4+459 x^3+2403 x^2-5250 x+1726}{3 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

-(1726 - 5250*x + 2403*x^2 + 459*x^3 + 81*x^4)/(3*(1 - 2*x)^(3/2))

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Maple [A]  time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{81\,{x}^{4}+459\,{x}^{3}+2403\,{x}^{2}-5250\,x+1726}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3*(81*x^4+459*x^3+2403*x^2-5250*x+1726)/(1-2*x)^(3/2)

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Maxima [A]  time = 1.35342, size = 57, normalized size = 0.86 \[ -\frac{27}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{207}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1071}{4} \, \sqrt{-2 \, x + 1} + \frac{49 \,{\left (804 \, x - 325\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/16*(-2*x + 1)^(5/2) + 207/8*(-2*x + 1)^(3/2) - 1071/4*sqrt(-2*x + 1) + 49/48
*(804*x - 325)/(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.222977, size = 49, normalized size = 0.74 \[ \frac{81 \, x^{4} + 459 \, x^{3} + 2403 \, x^{2} - 5250 \, x + 1726}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*(81*x^4 + 459*x^3 + 2403*x^2 - 5250*x + 1726)/((2*x - 1)*sqrt(-2*x + 1))

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{3} \left (5 x + 3\right )}{\left (- 2 x + 1\right )^{\frac{5}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Integral((3*x + 2)**3*(5*x + 3)/(-2*x + 1)**(5/2), x)

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GIAC/XCAS [A]  time = 0.212248, size = 76, normalized size = 1.15 \[ -\frac{27}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{207}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1071}{4} \, \sqrt{-2 \, x + 1} - \frac{49 \,{\left (804 \, x - 325\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/16*(2*x - 1)^2*sqrt(-2*x + 1) + 207/8*(-2*x + 1)^(3/2) - 1071/4*sqrt(-2*x +
1) - 49/48*(804*x - 325)/((2*x - 1)*sqrt(-2*x + 1))