Optimal. Leaf size=13 \[ \frac{2}{3} \left (\sqrt{x}+1\right )^3 \]
[Out]
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Rubi [A] time = 0.0103076, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{2}{3} \left (\sqrt{x}+1\right )^3 \]
Antiderivative was successfully verified.
[In] Int[(1 + Sqrt[x])^2/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 1.66702, size = 10, normalized size = 0.77 \[ \frac{2 \left (\sqrt{x} + 1\right )^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x**(1/2))**2/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0037662, size = 20, normalized size = 1.54 \[ \frac{2 x^{3/2}}{3}+2 x+2 \sqrt{x} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + Sqrt[x])^2/Sqrt[x],x]
[Out]
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Maple [A] time = 0.003, size = 15, normalized size = 1.2 \[{\frac{2}{3}{x}^{{\frac{3}{2}}}}+2\,x+2\,\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x^(1/2))^2/x^(1/2),x)
[Out]
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Maxima [A] time = 1.43368, size = 12, normalized size = 0.92 \[ \frac{2}{3} \,{\left (\sqrt{x} + 1\right )}^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((sqrt(x) + 1)^2/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235999, size = 16, normalized size = 1.23 \[ \frac{2}{3} \,{\left (x + 3\right )} \sqrt{x} + 2 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((sqrt(x) + 1)^2/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.328288, size = 17, normalized size = 1.31 \[ \frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + 2 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x**(1/2))**2/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.257539, size = 19, normalized size = 1.46 \[ \frac{2}{3} \, x^{\frac{3}{2}} + 2 \, x + 2 \, \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((sqrt(x) + 1)^2/sqrt(x),x, algorithm="giac")
[Out]