3.2079 \(\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx\)

Optimal. Leaf size=79 \[ \frac{125}{32} (1-2 x)^{9/2}-\frac{12675}{224} (1-2 x)^{7/2}+\frac{5711}{16} (1-2 x)^{5/2}-\frac{21439}{16} (1-2 x)^{3/2}+\frac{144837}{32} \sqrt{1-2 x}+\frac{65219}{32 \sqrt{1-2 x}} \]

[Out]

65219/(32*Sqrt[1 - 2*x]) + (144837*Sqrt[1 - 2*x])/32 - (21439*(1 - 2*x)^(3/2))/1
6 + (5711*(1 - 2*x)^(5/2))/16 - (12675*(1 - 2*x)^(7/2))/224 + (125*(1 - 2*x)^(9/
2))/32

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Rubi [A]  time = 0.0707924, 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 \[ \frac{125}{32} (1-2 x)^{9/2}-\frac{12675}{224} (1-2 x)^{7/2}+\frac{5711}{16} (1-2 x)^{5/2}-\frac{21439}{16} (1-2 x)^{3/2}+\frac{144837}{32} \sqrt{1-2 x}+\frac{65219}{32 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

65219/(32*Sqrt[1 - 2*x]) + (144837*Sqrt[1 - 2*x])/32 - (21439*(1 - 2*x)^(3/2))/1
6 + (5711*(1 - 2*x)^(5/2))/16 - (12675*(1 - 2*x)^(7/2))/224 + (125*(1 - 2*x)^(9/
2))/32

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Rubi in Sympy [A]  time = 9.31857, size = 70, normalized size = 0.89 \[ \frac{125 \left (- 2 x + 1\right )^{\frac{9}{2}}}{32} - \frac{12675 \left (- 2 x + 1\right )^{\frac{7}{2}}}{224} + \frac{5711 \left (- 2 x + 1\right )^{\frac{5}{2}}}{16} - \frac{21439 \left (- 2 x + 1\right )^{\frac{3}{2}}}{16} + \frac{144837 \sqrt{- 2 x + 1}}{32} + \frac{65219}{32 \sqrt{- 2 x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125*(-2*x + 1)**(9/2)/32 - 12675*(-2*x + 1)**(7/2)/224 + 5711*(-2*x + 1)**(5/2)/
16 - 21439*(-2*x + 1)**(3/2)/16 + 144837*sqrt(-2*x + 1)/32 + 65219/(32*sqrt(-2*x
+ 1))

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Mathematica [A]  time = 0.0513531, size = 38, normalized size = 0.48 \[ \frac{-875 x^5-4150 x^4-9501 x^3-15948 x^2-37944 x+38700}{7 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

(38700 - 37944*x - 15948*x^2 - 9501*x^3 - 4150*x^4 - 875*x^5)/(7*Sqrt[1 - 2*x])

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Maple [A]  time = 0.006, size = 35, normalized size = 0.4 \[ -{\frac{875\,{x}^{5}+4150\,{x}^{4}+9501\,{x}^{3}+15948\,{x}^{2}+37944\,x-38700}{7}{\frac{1}{\sqrt{1-2\,x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/7*(875*x^5+4150*x^4+9501*x^3+15948*x^2+37944*x-38700)/(1-2*x)^(1/2)

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Maxima [A]  time = 1.34642, size = 74, normalized size = 0.94 \[ \frac{125}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{12675}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{5711}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{21439}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{144837}{32} \, \sqrt{-2 \, x + 1} + \frac{65219}{32 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/32*(-2*x + 1)^(9/2) - 12675/224*(-2*x + 1)^(7/2) + 5711/16*(-2*x + 1)^(5/2)
- 21439/16*(-2*x + 1)^(3/2) + 144837/32*sqrt(-2*x + 1) + 65219/32/sqrt(-2*x + 1)

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Fricas [A]  time = 0.216668, size = 46, normalized size = 0.58 \[ -\frac{875 \, x^{5} + 4150 \, x^{4} + 9501 \, x^{3} + 15948 \, x^{2} + 37944 \, x - 38700}{7 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/7*(875*x^5 + 4150*x^4 + 9501*x^3 + 15948*x^2 + 37944*x - 38700)/sqrt(-2*x + 1
)

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.216887, size = 103, normalized size = 1.3 \[ \frac{125}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{12675}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{5711}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{21439}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{144837}{32} \, \sqrt{-2 \, x + 1} + \frac{65219}{32 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/32*(2*x - 1)^4*sqrt(-2*x + 1) + 12675/224*(2*x - 1)^3*sqrt(-2*x + 1) + 5711/
16*(2*x - 1)^2*sqrt(-2*x + 1) - 21439/16*(-2*x + 1)^(3/2) + 144837/32*sqrt(-2*x
+ 1) + 65219/32/sqrt(-2*x + 1)