3.1778 \(\int \sqrt{1-2 x} (2+3 x) (3+5 x) \, dx\)

Optimal. Leaf size=40 \[ -\frac{15}{28} (1-2 x)^{7/2}+\frac{17}{5} (1-2 x)^{5/2}-\frac{77}{12} (1-2 x)^{3/2} \]

[Out]

(-77*(1 - 2*x)^(3/2))/12 + (17*(1 - 2*x)^(5/2))/5 - (15*(1 - 2*x)^(7/2))/28

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Rubi [A]  time = 0.033172, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{15}{28} (1-2 x)^{7/2}+\frac{17}{5} (1-2 x)^{5/2}-\frac{77}{12} (1-2 x)^{3/2} \]

Antiderivative was successfully verified.

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

[Out]

(-77*(1 - 2*x)^(3/2))/12 + (17*(1 - 2*x)^(5/2))/5 - (15*(1 - 2*x)^(7/2))/28

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Rubi in Sympy [A]  time = 5.58375, size = 34, normalized size = 0.85 \[ - \frac{15 \left (- 2 x + 1\right )^{\frac{7}{2}}}{28} + \frac{17 \left (- 2 x + 1\right )^{\frac{5}{2}}}{5} - \frac{77 \left (- 2 x + 1\right )^{\frac{3}{2}}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*(-2*x + 1)**(7/2)/28 + 17*(-2*x + 1)**(5/2)/5 - 77*(-2*x + 1)**(3/2)/12

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Mathematica [A]  time = 0.0122109, size = 23, normalized size = 0.57 \[ -\frac{1}{105} (1-2 x)^{3/2} \left (225 x^2+489 x+373\right ) \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(3/2)*(373 + 489*x + 225*x^2))/105

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Maple [A]  time = 0.005, size = 20, normalized size = 0.5 \[ -{\frac{225\,{x}^{2}+489\,x+373}{105} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(225*x^2+489*x+373)*(1-2*x)^(3/2)

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Maxima [A]  time = 1.35803, size = 38, normalized size = 0.95 \[ -\frac{15}{28} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{17}{5} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{77}{12} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/28*(-2*x + 1)^(7/2) + 17/5*(-2*x + 1)^(5/2) - 77/12*(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.204952, size = 32, normalized size = 0.8 \[ \frac{1}{105} \,{\left (450 \, x^{3} + 753 \, x^{2} + 257 \, x - 373\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/105*(450*x^3 + 753*x^2 + 257*x - 373)*sqrt(-2*x + 1)

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Sympy [A]  time = 2.9254, size = 34, normalized size = 0.85 \[ - \frac{15 \left (- 2 x + 1\right )^{\frac{7}{2}}}{28} + \frac{17 \left (- 2 x + 1\right )^{\frac{5}{2}}}{5} - \frac{77 \left (- 2 x + 1\right )^{\frac{3}{2}}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*(-2*x + 1)**(7/2)/28 + 17*(-2*x + 1)**(5/2)/5 - 77*(-2*x + 1)**(3/2)/12

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GIAC/XCAS [A]  time = 0.214296, size = 57, normalized size = 1.42 \[ \frac{15}{28} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{17}{5} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{77}{12} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

15/28*(2*x - 1)^3*sqrt(-2*x + 1) + 17/5*(2*x - 1)^2*sqrt(-2*x + 1) - 77/12*(-2*x
+ 1)^(3/2)