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