3.2119 \(\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^{5/2}} \, dx\)

Optimal. Leaf size=79 \[ \frac{405}{224} (1-2 x)^{7/2}-\frac{4671}{160} (1-2 x)^{5/2}+\frac{3591}{16} (1-2 x)^{3/2}-\frac{24843}{16} \sqrt{1-2 x}-\frac{57281}{32 \sqrt{1-2 x}}+\frac{26411}{96 (1-2 x)^{3/2}} \]

[Out]

26411/(96*(1 - 2*x)^(3/2)) - 57281/(32*Sqrt[1 - 2*x]) - (24843*Sqrt[1 - 2*x])/16
+ (3591*(1 - 2*x)^(3/2))/16 - (4671*(1 - 2*x)^(5/2))/160 + (405*(1 - 2*x)^(7/2)
)/224

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Rubi [A]  time = 0.0657786, antiderivative size = 79, 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 \[ \frac{405}{224} (1-2 x)^{7/2}-\frac{4671}{160} (1-2 x)^{5/2}+\frac{3591}{16} (1-2 x)^{3/2}-\frac{24843}{16} \sqrt{1-2 x}-\frac{57281}{32 \sqrt{1-2 x}}+\frac{26411}{96 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^(5/2),x]

[Out]

26411/(96*(1 - 2*x)^(3/2)) - 57281/(32*Sqrt[1 - 2*x]) - (24843*Sqrt[1 - 2*x])/16
+ (3591*(1 - 2*x)^(3/2))/16 - (4671*(1 - 2*x)^(5/2))/160 + (405*(1 - 2*x)^(7/2)
)/224

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Rubi in Sympy [A]  time = 8.97972, size = 70, normalized size = 0.89 \[ \frac{405 \left (- 2 x + 1\right )^{\frac{7}{2}}}{224} - \frac{4671 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} + \frac{3591 \left (- 2 x + 1\right )^{\frac{3}{2}}}{16} - \frac{24843 \sqrt{- 2 x + 1}}{16} - \frac{57281}{32 \sqrt{- 2 x + 1}} + \frac{26411}{96 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4*(3+5*x)/(1-2*x)**(5/2),x)

[Out]

405*(-2*x + 1)**(7/2)/224 - 4671*(-2*x + 1)**(5/2)/160 + 3591*(-2*x + 1)**(3/2)/
16 - 24843*sqrt(-2*x + 1)/16 - 57281/(32*sqrt(-2*x + 1)) + 26411/(96*(-2*x + 1)*
*(3/2))

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Mathematica [A]  time = 0.0291159, size = 38, normalized size = 0.48 \[ -\frac{6075 x^5+33858 x^4+105624 x^3+435312 x^2-909264 x+301408}{105 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^(5/2),x]

[Out]

-(301408 - 909264*x + 435312*x^2 + 105624*x^3 + 33858*x^4 + 6075*x^5)/(105*(1 -
2*x)^(3/2))

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Maple [A]  time = 0.006, size = 35, normalized size = 0.4 \[ -{\frac{6075\,{x}^{5}+33858\,{x}^{4}+105624\,{x}^{3}+435312\,{x}^{2}-909264\,x+301408}{105} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4*(3+5*x)/(1-2*x)^(5/2),x)

[Out]

-1/105*(6075*x^5+33858*x^4+105624*x^3+435312*x^2-909264*x+301408)/(1-2*x)^(3/2)

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Maxima [A]  time = 1.34824, size = 69, normalized size = 0.87 \[ \frac{405}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{4671}{160} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{3591}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{24843}{16} \, \sqrt{-2 \, x + 1} + \frac{343 \,{\left (501 \, x - 212\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="maxima")

[Out]

405/224*(-2*x + 1)^(7/2) - 4671/160*(-2*x + 1)^(5/2) + 3591/16*(-2*x + 1)^(3/2)
- 24843/16*sqrt(-2*x + 1) + 343/48*(501*x - 212)/(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.230323, size = 55, normalized size = 0.7 \[ \frac{6075 \, x^{5} + 33858 \, x^{4} + 105624 \, x^{3} + 435312 \, x^{2} - 909264 \, x + 301408}{105 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="fricas")

[Out]

1/105*(6075*x^5 + 33858*x^4 + 105624*x^3 + 435312*x^2 - 909264*x + 301408)/((2*x
- 1)*sqrt(-2*x + 1))

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{4} \left (5 x + 3\right )}{\left (- 2 x + 1\right )^{\frac{5}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4*(3+5*x)/(1-2*x)**(5/2),x)

[Out]

Integral((3*x + 2)**4*(5*x + 3)/(-2*x + 1)**(5/2), x)

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GIAC/XCAS [A]  time = 0.21538, size = 97, normalized size = 1.23 \[ -\frac{405}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{4671}{160} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{3591}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{24843}{16} \, \sqrt{-2 \, x + 1} - \frac{343 \,{\left (501 \, x - 212\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="giac")

[Out]

-405/224*(2*x - 1)^3*sqrt(-2*x + 1) - 4671/160*(2*x - 1)^2*sqrt(-2*x + 1) + 3591
/16*(-2*x + 1)^(3/2) - 24843/16*sqrt(-2*x + 1) - 343/48*(501*x - 212)/((2*x - 1)
*sqrt(-2*x + 1))