Optimal. Leaf size=29 \[ \frac{4}{3} \left (\sqrt{x}+1\right )^{3/2}-4 \sqrt{\sqrt{x}+1} \]
[Out]
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Rubi [A] time = 0.0177053, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{4}{3} \left (\sqrt{x}+1\right )^{3/2}-4 \sqrt{\sqrt{x}+1} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[1 + Sqrt[x]],x]
[Out]
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Rubi in Sympy [A] time = 1.05162, size = 24, normalized size = 0.83 \[ \frac{4 \left (\sqrt{x} + 1\right )^{\frac{3}{2}}}{3} - 4 \sqrt{\sqrt{x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+x**(1/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.00751384, size = 22, normalized size = 0.76 \[ \frac{4}{3} \left (\sqrt{x}-2\right ) \sqrt{\sqrt{x}+1} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[1 + Sqrt[x]],x]
[Out]
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Maple [A] time = 0.007, size = 20, normalized size = 0.7 \[{\frac{4}{3} \left ( 1+\sqrt{x} \right ) ^{{\frac{3}{2}}}}-4\,\sqrt{1+\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+x^(1/2))^(1/2),x)
[Out]
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Maxima [A] time = 1.33752, size = 26, normalized size = 0.9 \[ \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} - 4 \, \sqrt{\sqrt{x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(sqrt(x) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204602, size = 19, normalized size = 0.66 \[ \frac{4}{3} \, \sqrt{\sqrt{x} + 1}{\left (\sqrt{x} - 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(sqrt(x) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.43966, size = 117, normalized size = 4.03 \[ - \frac{4 x^{\frac{5}{2}} \sqrt{\sqrt{x} + 1}}{3 x^{\frac{5}{2}} + 3 x^{2}} + \frac{8 x^{\frac{5}{2}}}{3 x^{\frac{5}{2}} + 3 x^{2}} + \frac{4 x^{3} \sqrt{\sqrt{x} + 1}}{3 x^{\frac{5}{2}} + 3 x^{2}} - \frac{8 x^{2} \sqrt{\sqrt{x} + 1}}{3 x^{\frac{5}{2}} + 3 x^{2}} + \frac{8 x^{2}}{3 x^{\frac{5}{2}} + 3 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+x**(1/2))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.206516, size = 26, normalized size = 0.9 \[ \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} - 4 \, \sqrt{\sqrt{x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(sqrt(x) + 1),x, algorithm="giac")
[Out]