3.2131 \(\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx\)

Optimal. Leaf size=79 \[ \frac{675}{224} (1-2 x)^{7/2}-\frac{1539}{32} (1-2 x)^{5/2}+\frac{5847}{16} (1-2 x)^{3/2}-\frac{39977}{16} \sqrt{1-2 x}-\frac{91091}{32 \sqrt{1-2 x}}+\frac{41503}{96 (1-2 x)^{3/2}} \]

[Out]

41503/(96*(1 - 2*x)^(3/2)) - 91091/(32*Sqrt[1 - 2*x]) - (39977*Sqrt[1 - 2*x])/16
+ (5847*(1 - 2*x)^(3/2))/16 - (1539*(1 - 2*x)^(5/2))/32 + (675*(1 - 2*x)^(7/2))
/224

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Rubi [A]  time = 0.0748367, antiderivative size = 79, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{675}{224} (1-2 x)^{7/2}-\frac{1539}{32} (1-2 x)^{5/2}+\frac{5847}{16} (1-2 x)^{3/2}-\frac{39977}{16} \sqrt{1-2 x}-\frac{91091}{32 \sqrt{1-2 x}}+\frac{41503}{96 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

41503/(96*(1 - 2*x)^(3/2)) - 91091/(32*Sqrt[1 - 2*x]) - (39977*Sqrt[1 - 2*x])/16
+ (5847*(1 - 2*x)^(3/2))/16 - (1539*(1 - 2*x)^(5/2))/32 + (675*(1 - 2*x)^(7/2))
/224

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Rubi in Sympy [A]  time = 9.31587, size = 70, normalized size = 0.89 \[ \frac{675 \left (- 2 x + 1\right )^{\frac{7}{2}}}{224} - \frac{1539 \left (- 2 x + 1\right )^{\frac{5}{2}}}{32} + \frac{5847 \left (- 2 x + 1\right )^{\frac{3}{2}}}{16} - \frac{39977 \sqrt{- 2 x + 1}}{16} - \frac{91091}{32 \sqrt{- 2 x + 1}} + \frac{41503}{96 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*(-2*x + 1)**(7/2)/224 - 1539*(-2*x + 1)**(5/2)/32 + 5847*(-2*x + 1)**(3/2)/1
6 - 39977*sqrt(-2*x + 1)/16 - 91091/(32*sqrt(-2*x + 1)) + 41503/(96*(-2*x + 1)**
(3/2))

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Mathematica [A]  time = 0.053928, size = 38, normalized size = 0.48 \[ -\frac{2025 x^5+11097 x^4+34137 x^3+139497 x^2-290838 x+96442}{21 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

-(96442 - 290838*x + 139497*x^2 + 34137*x^3 + 11097*x^4 + 2025*x^5)/(21*(1 - 2*x
)^(3/2))

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Maple [A]  time = 0.006, size = 35, normalized size = 0.4 \[ -{\frac{2025\,{x}^{5}+11097\,{x}^{4}+34137\,{x}^{3}+139497\,{x}^{2}-290838\,x+96442}{21} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*(2025*x^5+11097*x^4+34137*x^3+139497*x^2-290838*x+96442)/(1-2*x)^(3/2)

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Maxima [A]  time = 1.33919, size = 69, normalized size = 0.87 \[ \frac{675}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{1539}{32} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{5847}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{39977}{16} \, \sqrt{-2 \, x + 1} + \frac{539 \,{\left (507 \, x - 215\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/224*(-2*x + 1)^(7/2) - 1539/32*(-2*x + 1)^(5/2) + 5847/16*(-2*x + 1)^(3/2) -
39977/16*sqrt(-2*x + 1) + 539/48*(507*x - 215)/(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.213025, size = 55, normalized size = 0.7 \[ \frac{2025 \, x^{5} + 11097 \, x^{4} + 34137 \, x^{3} + 139497 \, x^{2} - 290838 \, x + 96442}{21 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/21*(2025*x^5 + 11097*x^4 + 34137*x^3 + 139497*x^2 - 290838*x + 96442)/((2*x -
1)*sqrt(-2*x + 1))

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.211535, size = 97, normalized size = 1.23 \[ -\frac{675}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{1539}{32} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{5847}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{39977}{16} \, \sqrt{-2 \, x + 1} - \frac{539 \,{\left (507 \, x - 215\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-675/224*(2*x - 1)^3*sqrt(-2*x + 1) - 1539/32*(2*x - 1)^2*sqrt(-2*x + 1) + 5847/
16*(-2*x + 1)^(3/2) - 39977/16*sqrt(-2*x + 1) - 539/48*(507*x - 215)/((2*x - 1)*
sqrt(-2*x + 1))