3.2054 \(\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^{3/2}} \, dx\)

Optimal. Leaf size=92 \[ -\frac{1215}{704} (1-2 x)^{11/2}+\frac{117}{4} (1-2 x)^{9/2}-\frac{13905}{64} (1-2 x)^{7/2}+\frac{7497}{8} (1-2 x)^{5/2}-\frac{173215}{64} (1-2 x)^{3/2}+\frac{60025}{8} \sqrt{1-2 x}+\frac{184877}{64 \sqrt{1-2 x}} \]

[Out]

184877/(64*Sqrt[1 - 2*x]) + (60025*Sqrt[1 - 2*x])/8 - (173215*(1 - 2*x)^(3/2))/6
4 + (7497*(1 - 2*x)^(5/2))/8 - (13905*(1 - 2*x)^(7/2))/64 + (117*(1 - 2*x)^(9/2)
)/4 - (1215*(1 - 2*x)^(11/2))/704

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Rubi [A]  time = 0.0723808, antiderivative size = 92, 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 \[ -\frac{1215}{704} (1-2 x)^{11/2}+\frac{117}{4} (1-2 x)^{9/2}-\frac{13905}{64} (1-2 x)^{7/2}+\frac{7497}{8} (1-2 x)^{5/2}-\frac{173215}{64} (1-2 x)^{3/2}+\frac{60025}{8} \sqrt{1-2 x}+\frac{184877}{64 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

184877/(64*Sqrt[1 - 2*x]) + (60025*Sqrt[1 - 2*x])/8 - (173215*(1 - 2*x)^(3/2))/6
4 + (7497*(1 - 2*x)^(5/2))/8 - (13905*(1 - 2*x)^(7/2))/64 + (117*(1 - 2*x)^(9/2)
)/4 - (1215*(1 - 2*x)^(11/2))/704

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Rubi in Sympy [A]  time = 10.5424, size = 82, normalized size = 0.89 \[ - \frac{1215 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{117 \left (- 2 x + 1\right )^{\frac{9}{2}}}{4} - \frac{13905 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} + \frac{7497 \left (- 2 x + 1\right )^{\frac{5}{2}}}{8} - \frac{173215 \left (- 2 x + 1\right )^{\frac{3}{2}}}{64} + \frac{60025 \sqrt{- 2 x + 1}}{8} + \frac{184877}{64 \sqrt{- 2 x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215*(-2*x + 1)**(11/2)/704 + 117*(-2*x + 1)**(9/2)/4 - 13905*(-2*x + 1)**(7/2)
/64 + 7497*(-2*x + 1)**(5/2)/8 - 173215*(-2*x + 1)**(3/2)/64 + 60025*sqrt(-2*x +
1)/8 + 184877/(64*sqrt(-2*x + 1))

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Mathematica [A]  time = 0.0445528, size = 47, normalized size = 0.51 \[ \frac{\sqrt{1-2 x} \left (1215 x^6+6651 x^5+17055 x^4+28692 x^3+41012 x^2+91704 x-92760\right )}{22 x-11} \]

Antiderivative was successfully verified.

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

[Out]

(Sqrt[1 - 2*x]*(-92760 + 91704*x + 41012*x^2 + 28692*x^3 + 17055*x^4 + 6651*x^5
+ 1215*x^6))/(-11 + 22*x)

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Maple [A]  time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{1215\,{x}^{6}+6651\,{x}^{5}+17055\,{x}^{4}+28692\,{x}^{3}+41012\,{x}^{2}+91704\,x-92760}{11}{\frac{1}{\sqrt{1-2\,x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/11*(1215*x^6+6651*x^5+17055*x^4+28692*x^3+41012*x^2+91704*x-92760)/(1-2*x)^(1
/2)

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Maxima [A]  time = 1.35549, size = 86, normalized size = 0.93 \[ -\frac{1215}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{117}{4} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{13905}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{7497}{8} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{173215}{64} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{60025}{8} \, \sqrt{-2 \, x + 1} + \frac{184877}{64 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215/704*(-2*x + 1)^(11/2) + 117/4*(-2*x + 1)^(9/2) - 13905/64*(-2*x + 1)^(7/2)
+ 7497/8*(-2*x + 1)^(5/2) - 173215/64*(-2*x + 1)^(3/2) + 60025/8*sqrt(-2*x + 1)
+ 184877/64/sqrt(-2*x + 1)

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Fricas [A]  time = 0.222261, size = 53, normalized size = 0.58 \[ -\frac{1215 \, x^{6} + 6651 \, x^{5} + 17055 \, x^{4} + 28692 \, x^{3} + 41012 \, x^{2} + 91704 \, x - 92760}{11 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/11*(1215*x^6 + 6651*x^5 + 17055*x^4 + 28692*x^3 + 41012*x^2 + 91704*x - 92760
)/sqrt(-2*x + 1)

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.2114, size = 124, normalized size = 1.35 \[ \frac{1215}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{117}{4} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{13905}{64} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{7497}{8} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{173215}{64} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{60025}{8} \, \sqrt{-2 \, x + 1} + \frac{184877}{64 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1215/704*(2*x - 1)^5*sqrt(-2*x + 1) + 117/4*(2*x - 1)^4*sqrt(-2*x + 1) + 13905/6
4*(2*x - 1)^3*sqrt(-2*x + 1) + 7497/8*(2*x - 1)^2*sqrt(-2*x + 1) - 173215/64*(-2
*x + 1)^(3/2) + 60025/8*sqrt(-2*x + 1) + 184877/64/sqrt(-2*x + 1)