3.2142 \(\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx\)

Optimal. Leaf size=92 \[ -\frac{375}{64} (1-2 x)^{9/2}+\frac{11475}{112} (1-2 x)^{7/2}-\frac{52011}{64} (1-2 x)^{5/2}+\frac{98209}{24} (1-2 x)^{3/2}-\frac{1334949}{64} \sqrt{1-2 x}-\frac{302379}{16 \sqrt{1-2 x}}+\frac{456533}{192 (1-2 x)^{3/2}} \]

[Out]

456533/(192*(1 - 2*x)^(3/2)) - 302379/(16*Sqrt[1 - 2*x]) - (1334949*Sqrt[1 - 2*x
])/64 + (98209*(1 - 2*x)^(3/2))/24 - (52011*(1 - 2*x)^(5/2))/64 + (11475*(1 - 2*
x)^(7/2))/112 - (375*(1 - 2*x)^(9/2))/64

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Rubi [A]  time = 0.0793596, antiderivative size = 92, 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 \[ -\frac{375}{64} (1-2 x)^{9/2}+\frac{11475}{112} (1-2 x)^{7/2}-\frac{52011}{64} (1-2 x)^{5/2}+\frac{98209}{24} (1-2 x)^{3/2}-\frac{1334949}{64} \sqrt{1-2 x}-\frac{302379}{16 \sqrt{1-2 x}}+\frac{456533}{192 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

456533/(192*(1 - 2*x)^(3/2)) - 302379/(16*Sqrt[1 - 2*x]) - (1334949*Sqrt[1 - 2*x
])/64 + (98209*(1 - 2*x)^(3/2))/24 - (52011*(1 - 2*x)^(5/2))/64 + (11475*(1 - 2*
x)^(7/2))/112 - (375*(1 - 2*x)^(9/2))/64

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Rubi in Sympy [A]  time = 10.2849, size = 82, normalized size = 0.89 \[ - \frac{375 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{11475 \left (- 2 x + 1\right )^{\frac{7}{2}}}{112} - \frac{52011 \left (- 2 x + 1\right )^{\frac{5}{2}}}{64} + \frac{98209 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{1334949 \sqrt{- 2 x + 1}}{64} - \frac{302379}{16 \sqrt{- 2 x + 1}} + \frac{456533}{192 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*(-2*x + 1)**(9/2)/64 + 11475*(-2*x + 1)**(7/2)/112 - 52011*(-2*x + 1)**(5/2
)/64 + 98209*(-2*x + 1)**(3/2)/24 - 1334949*sqrt(-2*x + 1)/64 - 302379/(16*sqrt(
-2*x + 1)) + 456533/(192*(-2*x + 1)**(3/2))

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Mathematica [A]  time = 0.0551084, size = 43, normalized size = 0.47 \[ -\frac{7875 x^6+45225 x^5+130464 x^4+293785 x^3+1051833 x^2-2146758 x+714074}{21 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

-(714074 - 2146758*x + 1051833*x^2 + 293785*x^3 + 130464*x^4 + 45225*x^5 + 7875*
x^6)/(21*(1 - 2*x)^(3/2))

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Maple [A]  time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{7875\,{x}^{6}+45225\,{x}^{5}+130464\,{x}^{4}+293785\,{x}^{3}+1051833\,{x}^{2}-2146758\,x+714074}{21} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*(7875*x^6+45225*x^5+130464*x^4+293785*x^3+1051833*x^2-2146758*x+714074)/(1
-2*x)^(3/2)

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Maxima [A]  time = 1.33184, size = 81, normalized size = 0.88 \[ -\frac{375}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{11475}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{52011}{64} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{98209}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1334949}{64} \, \sqrt{-2 \, x + 1} + \frac{5929 \,{\left (1224 \, x - 535\right )}}{192 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/64*(-2*x + 1)^(9/2) + 11475/112*(-2*x + 1)^(7/2) - 52011/64*(-2*x + 1)^(5/2
) + 98209/24*(-2*x + 1)^(3/2) - 1334949/64*sqrt(-2*x + 1) + 5929/192*(1224*x - 5
35)/(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.214212, size = 62, normalized size = 0.67 \[ \frac{7875 \, x^{6} + 45225 \, x^{5} + 130464 \, x^{4} + 293785 \, x^{3} + 1051833 \, x^{2} - 2146758 \, x + 714074}{21 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/21*(7875*x^6 + 45225*x^5 + 130464*x^4 + 293785*x^3 + 1051833*x^2 - 2146758*x +
714074)/((2*x - 1)*sqrt(-2*x + 1))

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.217623, size = 119, normalized size = 1.29 \[ -\frac{375}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{11475}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{52011}{64} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{98209}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1334949}{64} \, \sqrt{-2 \, x + 1} - \frac{5929 \,{\left (1224 \, x - 535\right )}}{192 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/64*(2*x - 1)^4*sqrt(-2*x + 1) - 11475/112*(2*x - 1)^3*sqrt(-2*x + 1) - 5201
1/64*(2*x - 1)^2*sqrt(-2*x + 1) + 98209/24*(-2*x + 1)^(3/2) - 1334949/64*sqrt(-2
*x + 1) - 5929/192*(1224*x - 535)/((2*x - 1)*sqrt(-2*x + 1))