3.1846 \(\int (1-2 x)^{3/2} (3+5 x) \, dx\)

Optimal. Leaf size=27 \[ \frac{5}{14} (1-2 x)^{7/2}-\frac{11}{10} (1-2 x)^{5/2} \]

[Out]

(-11*(1 - 2*x)^(5/2))/10 + (5*(1 - 2*x)^(7/2))/14

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Rubi [A]  time = 0.0184909, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{5}{14} (1-2 x)^{7/2}-\frac{11}{10} (1-2 x)^{5/2} \]

Antiderivative was successfully verified.

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

[Out]

(-11*(1 - 2*x)^(5/2))/10 + (5*(1 - 2*x)^(7/2))/14

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Rubi in Sympy [A]  time = 3.78904, size = 22, normalized size = 0.81 \[ \frac{5 \left (- 2 x + 1\right )^{\frac{7}{2}}}{14} - \frac{11 \left (- 2 x + 1\right )^{\frac{5}{2}}}{10} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*(-2*x + 1)**(7/2)/14 - 11*(-2*x + 1)**(5/2)/10

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Mathematica [A]  time = 0.010625, size = 18, normalized size = 0.67 \[ -\frac{1}{35} (1-2 x)^{5/2} (25 x+26) \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(5/2)*(26 + 25*x))/35

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Maple [A]  time = 0.004, size = 15, normalized size = 0.6 \[ -{\frac{25\,x+26}{35} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^(3/2)*(3+5*x),x)

[Out]

-1/35*(25*x+26)*(1-2*x)^(5/2)

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Maxima [A]  time = 1.37885, size = 26, normalized size = 0.96 \[ \frac{5}{14} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{11}{10} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/14*(-2*x + 1)^(7/2) - 11/10*(-2*x + 1)^(5/2)

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Fricas [A]  time = 0.222322, size = 32, normalized size = 1.19 \[ -\frac{1}{35} \,{\left (100 \, x^{3} + 4 \, x^{2} - 79 \, x + 26\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/35*(100*x^3 + 4*x^2 - 79*x + 26)*sqrt(-2*x + 1)

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Sympy [A]  time = 1.07133, size = 54, normalized size = 2. \[ - \frac{20 x^{3} \sqrt{- 2 x + 1}}{7} - \frac{4 x^{2} \sqrt{- 2 x + 1}}{35} + \frac{79 x \sqrt{- 2 x + 1}}{35} - \frac{26 \sqrt{- 2 x + 1}}{35} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20*x**3*sqrt(-2*x + 1)/7 - 4*x**2*sqrt(-2*x + 1)/35 + 79*x*sqrt(-2*x + 1)/35 -
26*sqrt(-2*x + 1)/35

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GIAC/XCAS [A]  time = 0.229932, size = 45, normalized size = 1.67 \[ -\frac{5}{14} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{11}{10} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/14*(2*x - 1)^3*sqrt(-2*x + 1) - 11/10*(2*x - 1)^2*sqrt(-2*x + 1)