3.1928 \(\int (1-2 x)^{5/2} (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=53 \[ \frac{75}{104} (1-2 x)^{13/2}-\frac{505}{88} (1-2 x)^{11/2}+\frac{1133}{72} (1-2 x)^{9/2}-\frac{121}{8} (1-2 x)^{7/2} \]

[Out]

(-121*(1 - 2*x)^(7/2))/8 + (1133*(1 - 2*x)^(9/2))/72 - (505*(1 - 2*x)^(11/2))/88
+ (75*(1 - 2*x)^(13/2))/104

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Rubi [A]  time = 0.0500025, antiderivative size = 53, 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 \[ \frac{75}{104} (1-2 x)^{13/2}-\frac{505}{88} (1-2 x)^{11/2}+\frac{1133}{72} (1-2 x)^{9/2}-\frac{121}{8} (1-2 x)^{7/2} \]

Antiderivative was successfully verified.

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

[Out]

(-121*(1 - 2*x)^(7/2))/8 + (1133*(1 - 2*x)^(9/2))/72 - (505*(1 - 2*x)^(11/2))/88
+ (75*(1 - 2*x)^(13/2))/104

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Rubi in Sympy [A]  time = 6.96746, size = 46, normalized size = 0.87 \[ \frac{75 \left (- 2 x + 1\right )^{\frac{13}{2}}}{104} - \frac{505 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} + \frac{1133 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} - \frac{121 \left (- 2 x + 1\right )^{\frac{7}{2}}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75*(-2*x + 1)**(13/2)/104 - 505*(-2*x + 1)**(11/2)/88 + 1133*(-2*x + 1)**(9/2)/7
2 - 121*(-2*x + 1)**(7/2)/8

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Mathematica [A]  time = 0.0418346, size = 28, normalized size = 0.53 \[ -\frac{(1-2 x)^{7/2} \left (7425 x^3+18405 x^2+16531 x+5671\right )}{1287} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(7/2)*(5671 + 16531*x + 18405*x^2 + 7425*x^3))/1287

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Maple [A]  time = 0.004, size = 25, normalized size = 0.5 \[ -{\frac{7425\,{x}^{3}+18405\,{x}^{2}+16531\,x+5671}{1287} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1287*(7425*x^3+18405*x^2+16531*x+5671)*(1-2*x)^(7/2)

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Maxima [A]  time = 1.3402, size = 50, normalized size = 0.94 \[ \frac{75}{104} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{505}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{1133}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{121}{8} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75/104*(-2*x + 1)^(13/2) - 505/88*(-2*x + 1)^(11/2) + 1133/72*(-2*x + 1)^(9/2) -
121/8*(-2*x + 1)^(7/2)

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Fricas [A]  time = 0.211826, size = 53, normalized size = 1. \[ \frac{1}{1287} \,{\left (59400 \, x^{6} + 58140 \, x^{5} - 44062 \, x^{4} - 49999 \, x^{3} + 12729 \, x^{2} + 17495 \, x - 5671\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1287*(59400*x^6 + 58140*x^5 - 44062*x^4 - 49999*x^3 + 12729*x^2 + 17495*x - 56
71)*sqrt(-2*x + 1)

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Sympy [A]  time = 2.89975, size = 100, normalized size = 1.89 \[ \frac{600 x^{6} \sqrt{- 2 x + 1}}{13} + \frac{6460 x^{5} \sqrt{- 2 x + 1}}{143} - \frac{44062 x^{4} \sqrt{- 2 x + 1}}{1287} - \frac{49999 x^{3} \sqrt{- 2 x + 1}}{1287} + \frac{4243 x^{2} \sqrt{- 2 x + 1}}{429} + \frac{17495 x \sqrt{- 2 x + 1}}{1287} - \frac{5671 \sqrt{- 2 x + 1}}{1287} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

600*x**6*sqrt(-2*x + 1)/13 + 6460*x**5*sqrt(-2*x + 1)/143 - 44062*x**4*sqrt(-2*x
+ 1)/1287 - 49999*x**3*sqrt(-2*x + 1)/1287 + 4243*x**2*sqrt(-2*x + 1)/429 + 174
95*x*sqrt(-2*x + 1)/1287 - 5671*sqrt(-2*x + 1)/1287

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GIAC/XCAS [A]  time = 0.23299, size = 88, normalized size = 1.66 \[ \frac{75}{104} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{505}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{1133}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{121}{8} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75/104*(2*x - 1)^6*sqrt(-2*x + 1) + 505/88*(2*x - 1)^5*sqrt(-2*x + 1) + 1133/72*
(2*x - 1)^4*sqrt(-2*x + 1) + 121/8*(2*x - 1)^3*sqrt(-2*x + 1)