3.1917 \(\int (1-2 x)^{5/2} (3+5 x) \, dx\)

Optimal. Leaf size=27 \[ \frac{5}{18} (1-2 x)^{9/2}-\frac{11}{14} (1-2 x)^{7/2} \]

[Out]

(-11*(1 - 2*x)^(7/2))/14 + (5*(1 - 2*x)^(9/2))/18

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Rubi [A]  time = 0.0211112, 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 \[ \frac{5}{18} (1-2 x)^{9/2}-\frac{11}{14} (1-2 x)^{7/2} \]

Antiderivative was successfully verified.

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

[Out]

(-11*(1 - 2*x)^(7/2))/14 + (5*(1 - 2*x)^(9/2))/18

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Rubi in Sympy [A]  time = 3.91119, size = 22, normalized size = 0.81 \[ \frac{5 \left (- 2 x + 1\right )^{\frac{9}{2}}}{18} - \frac{11 \left (- 2 x + 1\right )^{\frac{7}{2}}}{14} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*(-2*x + 1)**(9/2)/18 - 11*(-2*x + 1)**(7/2)/14

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Mathematica [A]  time = 0.0120454, size = 18, normalized size = 0.67 \[ -\frac{1}{63} (1-2 x)^{7/2} (35 x+32) \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(7/2)*(32 + 35*x))/63

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Maple [A]  time = 0.003, size = 15, normalized size = 0.6 \[ -{\frac{35\,x+32}{63} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^(5/2)*(3+5*x),x)

[Out]

-1/63*(35*x+32)*(1-2*x)^(7/2)

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Maxima [A]  time = 1.34984, size = 26, normalized size = 0.96 \[ \frac{5}{18} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{11}{14} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/18*(-2*x + 1)^(9/2) - 11/14*(-2*x + 1)^(7/2)

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Fricas [A]  time = 0.206911, size = 39, normalized size = 1.44 \[ \frac{1}{63} \,{\left (280 \, x^{4} - 164 \, x^{3} - 174 \, x^{2} + 157 \, x - 32\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/63*(280*x^4 - 164*x^3 - 174*x^2 + 157*x - 32)*sqrt(-2*x + 1)

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Sympy [A]  time = 1.62297, size = 70, normalized size = 2.59 \[ \frac{40 x^{4} \sqrt{- 2 x + 1}}{9} - \frac{164 x^{3} \sqrt{- 2 x + 1}}{63} - \frac{58 x^{2} \sqrt{- 2 x + 1}}{21} + \frac{157 x \sqrt{- 2 x + 1}}{63} - \frac{32 \sqrt{- 2 x + 1}}{63} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

40*x**4*sqrt(-2*x + 1)/9 - 164*x**3*sqrt(-2*x + 1)/63 - 58*x**2*sqrt(-2*x + 1)/2
1 + 157*x*sqrt(-2*x + 1)/63 - 32*sqrt(-2*x + 1)/63

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GIAC/XCAS [A]  time = 0.207716, size = 45, normalized size = 1.67 \[ \frac{5}{18} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{11}{14} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/18*(2*x - 1)^4*sqrt(-2*x + 1) + 11/14*(2*x - 1)^3*sqrt(-2*x + 1)