3.702 \(\int \sqrt{1-x} \, dx\)

Optimal. Leaf size=13 \[ -\frac{2}{3} (1-x)^{3/2} \]

[Out]

(-2*(1 - x)^(3/2))/3

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Rubi [A]  time = 0.00545891, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{2}{3} (1-x)^{3/2} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[1 - x],x]

[Out]

(-2*(1 - x)^(3/2))/3

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Rubi in Sympy [A]  time = 0.532459, size = 10, normalized size = 0.77 \[ - \frac{2 \left (- x + 1\right )^{\frac{3}{2}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-x)**(1/2),x)

[Out]

-2*(-x + 1)**(3/2)/3

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Mathematica [A]  time = 0.00247891, size = 13, normalized size = 1. \[ -\frac{2}{3} (1-x)^{3/2} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[1 - x],x]

[Out]

(-2*(1 - x)^(3/2))/3

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Maple [A]  time = 0.002, size = 10, normalized size = 0.8 \[ -{\frac{2}{3} \left ( 1-x \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-x)^(1/2),x)

[Out]

-2/3*(1-x)^(3/2)

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Maxima [A]  time = 0.68239, size = 12, normalized size = 0.92 \[ -\frac{2}{3} \,{\left (-x + 1\right )}^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/3*(-x + 1)^(3/2)

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Fricas [A]  time = 0.270825, size = 16, normalized size = 1.23 \[ \frac{2}{3} \,{\left (x - 1\right )} \sqrt{-x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/3*(x - 1)*sqrt(-x + 1)

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Sympy [A]  time = 0.068271, size = 10, normalized size = 0.77 \[ - \frac{2 \left (- x + 1\right )^{\frac{3}{2}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-x)**(1/2),x)

[Out]

-2*(-x + 1)**(3/2)/3

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GIAC/XCAS [A]  time = 0.263411, size = 12, normalized size = 0.92 \[ -\frac{2}{3} \,{\left (-x + 1\right )}^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/3*(-x + 1)^(3/2)