3.1789 \(\int \sqrt{1-2 x} (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=53 \[ \frac{25}{24} (1-2 x)^{9/2}-\frac{505}{56} (1-2 x)^{7/2}+\frac{1133}{40} (1-2 x)^{5/2}-\frac{847}{24} (1-2 x)^{3/2} \]

[Out]

(-847*(1 - 2*x)^(3/2))/24 + (1133*(1 - 2*x)^(5/2))/40 - (505*(1 - 2*x)^(7/2))/56
+ (25*(1 - 2*x)^(9/2))/24

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Rubi [A]  time = 0.0443285, 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 \[ \frac{25}{24} (1-2 x)^{9/2}-\frac{505}{56} (1-2 x)^{7/2}+\frac{1133}{40} (1-2 x)^{5/2}-\frac{847}{24} (1-2 x)^{3/2} \]

Antiderivative was successfully verified.

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

[Out]

(-847*(1 - 2*x)^(3/2))/24 + (1133*(1 - 2*x)^(5/2))/40 - (505*(1 - 2*x)^(7/2))/56
+ (25*(1 - 2*x)^(9/2))/24

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Rubi in Sympy [A]  time = 6.85334, size = 46, normalized size = 0.87 \[ \frac{25 \left (- 2 x + 1\right )^{\frac{9}{2}}}{24} - \frac{505 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} + \frac{1133 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} - \frac{847 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25*(-2*x + 1)**(9/2)/24 - 505*(-2*x + 1)**(7/2)/56 + 1133*(-2*x + 1)**(5/2)/40 -
847*(-2*x + 1)**(3/2)/24

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Mathematica [A]  time = 0.0271067, size = 33, normalized size = 0.62 \[ \frac{1}{105} \sqrt{1-2 x} \left (1750 x^4+4075 x^3+3159 x^2+321 x-1569\right ) \]

Antiderivative was successfully verified.

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

[Out]

(Sqrt[1 - 2*x]*(-1569 + 321*x + 3159*x^2 + 4075*x^3 + 1750*x^4))/105

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Maple [A]  time = 0.006, size = 25, normalized size = 0.5 \[ -{\frac{875\,{x}^{3}+2475\,{x}^{2}+2817\,x+1569}{105} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(875*x^3+2475*x^2+2817*x+1569)*(1-2*x)^(3/2)

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Maxima [A]  time = 1.34543, size = 50, normalized size = 0.94 \[ \frac{25}{24} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{505}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{1133}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{847}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/24*(-2*x + 1)^(9/2) - 505/56*(-2*x + 1)^(7/2) + 1133/40*(-2*x + 1)^(5/2) - 84
7/24*(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.209659, size = 39, normalized size = 0.74 \[ \frac{1}{105} \,{\left (1750 \, x^{4} + 4075 \, x^{3} + 3159 \, x^{2} + 321 \, x - 1569\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/105*(1750*x^4 + 4075*x^3 + 3159*x^2 + 321*x - 1569)*sqrt(-2*x + 1)

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Sympy [A]  time = 2.84287, size = 46, normalized size = 0.87 \[ \frac{25 \left (- 2 x + 1\right )^{\frac{9}{2}}}{24} - \frac{505 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} + \frac{1133 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} - \frac{847 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25*(-2*x + 1)**(9/2)/24 - 505*(-2*x + 1)**(7/2)/56 + 1133*(-2*x + 1)**(5/2)/40 -
847*(-2*x + 1)**(3/2)/24

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GIAC/XCAS [A]  time = 0.211764, size = 78, normalized size = 1.47 \[ \frac{25}{24} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{505}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{1133}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{847}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/24*(2*x - 1)^4*sqrt(-2*x + 1) + 505/56*(2*x - 1)^3*sqrt(-2*x + 1) + 1133/40*(
2*x - 1)^2*sqrt(-2*x + 1) - 847/24*(-2*x + 1)^(3/2)