3.693 \(\int \frac{1-x}{1+\sqrt{x}} \, dx\)

Optimal. Leaf size=11 \[ x-\frac{2 x^{3/2}}{3} \]

[Out]

x - (2*x^(3/2))/3

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Rubi [A]  time = 0.0216977, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ x-\frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]  Int[(1 - x)/(1 + Sqrt[x]),x]

[Out]

x - (2*x^(3/2))/3

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{2 x^{\frac{3}{2}}}{3} + 2 \int ^{\sqrt{x}} x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*x**(3/2)/3 + 2*Integral(x, (x, sqrt(x)))

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Mathematica [A]  time = 0.000793878, size = 11, normalized size = 1. \[ x-\frac{2 x^{3/2}}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - x)/(1 + Sqrt[x]),x]

[Out]

x - (2*x^(3/2))/3

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Maple [A]  time = 0.002, size = 8, normalized size = 0.7 \[ x-{\frac{2}{3}{x}^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-x)/(1+x^(1/2)),x)

[Out]

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

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Maxima [A]  time = 0.675083, size = 9, normalized size = 0.82 \[ -\frac{2}{3} \, x^{\frac{3}{2}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/3*x^(3/2) + x

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Fricas [A]  time = 0.261059, size = 9, normalized size = 0.82 \[ -\frac{2}{3} \, x^{\frac{3}{2}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/3*x^(3/2) + x

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Sympy [A]  time = 2.91155, size = 22, normalized size = 2. \[ - \frac{2 \sqrt{x} \left (x - 1\right )}{3} - \frac{2 \sqrt{x}}{3} + x - 1 \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-x)/(1+x**(1/2)),x)

[Out]

-2*sqrt(x)*(x - 1)/3 - 2*sqrt(x)/3 + x - 1

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GIAC/XCAS [A]  time = 0.263503, size = 9, normalized size = 0.82 \[ -\frac{2}{3} \, x^{\frac{3}{2}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/3*x^(3/2) + x