3.2143 \(\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx\)

Optimal. Leaf size=79 \[ \frac{1125}{224} (1-2 x)^{7/2}-\frac{2535}{32} (1-2 x)^{5/2}+\frac{28555}{48} (1-2 x)^{3/2}-\frac{64317}{16} \sqrt{1-2 x}-\frac{144837}{32 \sqrt{1-2 x}}+\frac{65219}{96 (1-2 x)^{3/2}} \]

[Out]

65219/(96*(1 - 2*x)^(3/2)) - 144837/(32*Sqrt[1 - 2*x]) - (64317*Sqrt[1 - 2*x])/1
6 + (28555*(1 - 2*x)^(3/2))/48 - (2535*(1 - 2*x)^(5/2))/32 + (1125*(1 - 2*x)^(7/
2))/224

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Rubi [A]  time = 0.0735289, 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 \[ \frac{1125}{224} (1-2 x)^{7/2}-\frac{2535}{32} (1-2 x)^{5/2}+\frac{28555}{48} (1-2 x)^{3/2}-\frac{64317}{16} \sqrt{1-2 x}-\frac{144837}{32 \sqrt{1-2 x}}+\frac{65219}{96 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

65219/(96*(1 - 2*x)^(3/2)) - 144837/(32*Sqrt[1 - 2*x]) - (64317*Sqrt[1 - 2*x])/1
6 + (28555*(1 - 2*x)^(3/2))/48 - (2535*(1 - 2*x)^(5/2))/32 + (1125*(1 - 2*x)^(7/
2))/224

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Rubi in Sympy [A]  time = 9.65914, size = 70, normalized size = 0.89 \[ \frac{1125 \left (- 2 x + 1\right )^{\frac{7}{2}}}{224} - \frac{2535 \left (- 2 x + 1\right )^{\frac{5}{2}}}{32} + \frac{28555 \left (- 2 x + 1\right )^{\frac{3}{2}}}{48} - \frac{64317 \sqrt{- 2 x + 1}}{16} - \frac{144837}{32 \sqrt{- 2 x + 1}} + \frac{65219}{96 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125*(-2*x + 1)**(7/2)/224 - 2535*(-2*x + 1)**(5/2)/32 + 28555*(-2*x + 1)**(3/2)
/48 - 64317*sqrt(-2*x + 1)/16 - 144837/(32*sqrt(-2*x + 1)) + 65219/(96*(-2*x + 1
)**(3/2))

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Mathematica [A]  time = 0.0542563, size = 38, normalized size = 0.48 \[ -\frac{3375 x^5+18180 x^4+55145 x^3+223458 x^2-465060 x+154264}{21 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

-(154264 - 465060*x + 223458*x^2 + 55145*x^3 + 18180*x^4 + 3375*x^5)/(21*(1 - 2*
x)^(3/2))

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Maple [A]  time = 0.006, size = 35, normalized size = 0.4 \[ -{\frac{3375\,{x}^{5}+18180\,{x}^{4}+55145\,{x}^{3}+223458\,{x}^{2}-465060\,x+154264}{21} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*(3375*x^5+18180*x^4+55145*x^3+223458*x^2-465060*x+154264)/(1-2*x)^(3/2)

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Maxima [A]  time = 1.36983, size = 69, normalized size = 0.87 \[ \frac{1125}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{2535}{32} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{28555}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{64317}{16} \, \sqrt{-2 \, x + 1} + \frac{847 \,{\left (513 \, x - 218\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125/224*(-2*x + 1)^(7/2) - 2535/32*(-2*x + 1)^(5/2) + 28555/48*(-2*x + 1)^(3/2)
- 64317/16*sqrt(-2*x + 1) + 847/48*(513*x - 218)/(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.214403, size = 55, normalized size = 0.7 \[ \frac{3375 \, x^{5} + 18180 \, x^{4} + 55145 \, x^{3} + 223458 \, x^{2} - 465060 \, x + 154264}{21 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/21*(3375*x^5 + 18180*x^4 + 55145*x^3 + 223458*x^2 - 465060*x + 154264)/((2*x -
1)*sqrt(-2*x + 1))

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.216948, size = 97, normalized size = 1.23 \[ -\frac{1125}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{2535}{32} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{28555}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{64317}{16} \, \sqrt{-2 \, x + 1} - \frac{847 \,{\left (513 \, x - 218\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1125/224*(2*x - 1)^3*sqrt(-2*x + 1) - 2535/32*(2*x - 1)^2*sqrt(-2*x + 1) + 2855
5/48*(-2*x + 1)^(3/2) - 64317/16*sqrt(-2*x + 1) - 847/48*(513*x - 218)/((2*x - 1
)*sqrt(-2*x + 1))