3.2078 \(\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{3/2}} \, dx\)

Optimal. Leaf size=92 \[ -\frac{3375}{704} (1-2 x)^{11/2}+\frac{1275}{16} (1-2 x)^{9/2}-\frac{260055}{448} (1-2 x)^{7/2}+\frac{98209}{40} (1-2 x)^{5/2}-\frac{444983}{64} (1-2 x)^{3/2}+\frac{302379}{16} \sqrt{1-2 x}+\frac{456533}{64 \sqrt{1-2 x}} \]

[Out]

456533/(64*Sqrt[1 - 2*x]) + (302379*Sqrt[1 - 2*x])/16 - (444983*(1 - 2*x)^(3/2))
/64 + (98209*(1 - 2*x)^(5/2))/40 - (260055*(1 - 2*x)^(7/2))/448 + (1275*(1 - 2*x
)^(9/2))/16 - (3375*(1 - 2*x)^(11/2))/704

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Rubi [A]  time = 0.0748616, 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 \[ -\frac{3375}{704} (1-2 x)^{11/2}+\frac{1275}{16} (1-2 x)^{9/2}-\frac{260055}{448} (1-2 x)^{7/2}+\frac{98209}{40} (1-2 x)^{5/2}-\frac{444983}{64} (1-2 x)^{3/2}+\frac{302379}{16} \sqrt{1-2 x}+\frac{456533}{64 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

456533/(64*Sqrt[1 - 2*x]) + (302379*Sqrt[1 - 2*x])/16 - (444983*(1 - 2*x)^(3/2))
/64 + (98209*(1 - 2*x)^(5/2))/40 - (260055*(1 - 2*x)^(7/2))/448 + (1275*(1 - 2*x
)^(9/2))/16 - (3375*(1 - 2*x)^(11/2))/704

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Rubi in Sympy [A]  time = 10.1847, size = 82, normalized size = 0.89 \[ - \frac{3375 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{1275 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} - \frac{260055 \left (- 2 x + 1\right )^{\frac{7}{2}}}{448} + \frac{98209 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} - \frac{444983 \left (- 2 x + 1\right )^{\frac{3}{2}}}{64} + \frac{302379 \sqrt{- 2 x + 1}}{16} + \frac{456533}{64 \sqrt{- 2 x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375*(-2*x + 1)**(11/2)/704 + 1275*(-2*x + 1)**(9/2)/16 - 260055*(-2*x + 1)**(7
/2)/448 + 98209*(-2*x + 1)**(5/2)/40 - 444983*(-2*x + 1)**(3/2)/64 + 302379*sqrt
(-2*x + 1)/16 + 456533/(64*sqrt(-2*x + 1))

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Mathematica [A]  time = 0.0552937, size = 43, normalized size = 0.47 \[ \frac{-118125 x^6-627375 x^5-1564350 x^4-2569643 x^3-3611453 x^2-8012926 x+8096086}{385 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

(8096086 - 8012926*x - 3611453*x^2 - 2569643*x^3 - 1564350*x^4 - 627375*x^5 - 11
8125*x^6)/(385*Sqrt[1 - 2*x])

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Maple [A]  time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{118125\,{x}^{6}+627375\,{x}^{5}+1564350\,{x}^{4}+2569643\,{x}^{3}+3611453\,{x}^{2}+8012926\,x-8096086}{385}{\frac{1}{\sqrt{1-2\,x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/385*(118125*x^6+627375*x^5+1564350*x^4+2569643*x^3+3611453*x^2+8012926*x-8096
086)/(1-2*x)^(1/2)

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Maxima [A]  time = 1.34886, size = 86, normalized size = 0.93 \[ -\frac{3375}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{1275}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{260055}{448} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{98209}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{444983}{64} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{302379}{16} \, \sqrt{-2 \, x + 1} + \frac{456533}{64 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375/704*(-2*x + 1)^(11/2) + 1275/16*(-2*x + 1)^(9/2) - 260055/448*(-2*x + 1)^(
7/2) + 98209/40*(-2*x + 1)^(5/2) - 444983/64*(-2*x + 1)^(3/2) + 302379/16*sqrt(-
2*x + 1) + 456533/64/sqrt(-2*x + 1)

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Fricas [A]  time = 0.219676, size = 53, normalized size = 0.58 \[ -\frac{118125 \, x^{6} + 627375 \, x^{5} + 1564350 \, x^{4} + 2569643 \, x^{3} + 3611453 \, x^{2} + 8012926 \, x - 8096086}{385 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/385*(118125*x^6 + 627375*x^5 + 1564350*x^4 + 2569643*x^3 + 3611453*x^2 + 8012
926*x - 8096086)/sqrt(-2*x + 1)

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.213132, size = 124, normalized size = 1.35 \[ \frac{3375}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{1275}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{260055}{448} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{98209}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{444983}{64} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{302379}{16} \, \sqrt{-2 \, x + 1} + \frac{456533}{64 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3375/704*(2*x - 1)^5*sqrt(-2*x + 1) + 1275/16*(2*x - 1)^4*sqrt(-2*x + 1) + 26005
5/448*(2*x - 1)^3*sqrt(-2*x + 1) + 98209/40*(2*x - 1)^2*sqrt(-2*x + 1) - 444983/
64*(-2*x + 1)^(3/2) + 302379/16*sqrt(-2*x + 1) + 456533/64/sqrt(-2*x + 1)