Optimal. Leaf size=15 \[ \frac{4}{3} \left (\sqrt{x}+1\right )^{3/2} \]
[Out]
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Rubi [A] time = 0.0115843, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{4}{3} \left (\sqrt{x}+1\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + Sqrt[x]]/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 1.68515, size = 12, normalized size = 0.8 \[ \frac{4 \left (\sqrt{x} + 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x**(1/2))**(1/2)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00515461, size = 15, normalized size = 1. \[ \frac{4}{3} \left (\sqrt{x}+1\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 + Sqrt[x]]/Sqrt[x],x]
[Out]
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Maple [A] time = 0.003, size = 10, normalized size = 0.7 \[{\frac{4}{3} \left ( 1+\sqrt{x} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x^(1/2))^(1/2)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.42043, size = 12, normalized size = 0.8 \[ \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x) + 1)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.24265, size = 12, normalized size = 0.8 \[ \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x) + 1)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.500026, size = 31, normalized size = 2.07 \[ \frac{4 \sqrt{x} \sqrt{\sqrt{x} + 1}}{3} + \frac{4 \sqrt{\sqrt{x} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x**(1/2))**(1/2)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.223076, size = 12, normalized size = 0.8 \[ \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x) + 1)/sqrt(x),x, algorithm="giac")
[Out]