Optimal. Leaf size=83 \[ \frac{8}{7} \left (\sqrt{\sqrt{x}+1}+2\right )^{7/2}-\frac{48}{5} \left (\sqrt{\sqrt{x}+1}+2\right )^{5/2}+\frac{88}{3} \left (\sqrt{\sqrt{x}+1}+2\right )^{3/2}-48 \sqrt{\sqrt{\sqrt{x}+1}+2} \]
[Out]
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Rubi [A] time = 0.101176, antiderivative size = 83, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ \frac{8}{7} \left (\sqrt{\sqrt{x}+1}+2\right )^{7/2}-\frac{48}{5} \left (\sqrt{\sqrt{x}+1}+2\right )^{5/2}+\frac{88}{3} \left (\sqrt{\sqrt{x}+1}+2\right )^{3/2}-48 \sqrt{\sqrt{\sqrt{x}+1}+2} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[2 + Sqrt[1 + Sqrt[x]]],x]
[Out]
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Rubi in Sympy [A] time = 4.69178, size = 71, normalized size = 0.86 \[ \frac{8 \left (\sqrt{\sqrt{x} + 1} + 2\right )^{\frac{7}{2}}}{7} - \frac{48 \left (\sqrt{\sqrt{x} + 1} + 2\right )^{\frac{5}{2}}}{5} + \frac{88 \left (\sqrt{\sqrt{x} + 1} + 2\right )^{\frac{3}{2}}}{3} - 48 \sqrt{\sqrt{\sqrt{x} + 1} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(2+(1+x**(1/2))**(1/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0162142, size = 58, normalized size = 0.7 \[ \frac{8}{105} \sqrt{\sqrt{\sqrt{x}+1}+2} \left (3 \sqrt{x} \left (5 \sqrt{\sqrt{x}+1}-12\right )+76 \sqrt{\sqrt{x}+1}-280\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[2 + Sqrt[1 + Sqrt[x]]],x]
[Out]
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Maple [A] time = 0., size = 54, normalized size = 0.7 \[{\frac{88}{3} \left ( 2+\sqrt{1+\sqrt{x}} \right ) ^{{\frac{3}{2}}}}-{\frac{48}{5} \left ( 2+\sqrt{1+\sqrt{x}} \right ) ^{{\frac{5}{2}}}}+{\frac{8}{7} \left ( 2+\sqrt{1+\sqrt{x}} \right ) ^{{\frac{7}{2}}}}-48\,\sqrt{2+\sqrt{1+\sqrt{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2+(1+x^(1/2))^(1/2))^(1/2),x)
[Out]
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Maxima [A] time = 0.735367, size = 72, normalized size = 0.87 \[ \frac{8}{7} \,{\left (\sqrt{\sqrt{x} + 1} + 2\right )}^{\frac{7}{2}} - \frac{48}{5} \,{\left (\sqrt{\sqrt{x} + 1} + 2\right )}^{\frac{5}{2}} + \frac{88}{3} \,{\left (\sqrt{\sqrt{x} + 1} + 2\right )}^{\frac{3}{2}} - 48 \, \sqrt{\sqrt{\sqrt{x} + 1} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(sqrt(sqrt(x) + 1) + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.268483, size = 47, normalized size = 0.57 \[ \frac{8}{105} \,{\left ({\left (15 \, \sqrt{x} + 76\right )} \sqrt{\sqrt{x} + 1} - 36 \, \sqrt{x} - 280\right )} \sqrt{\sqrt{\sqrt{x} + 1} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(sqrt(sqrt(x) + 1) + 2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{\sqrt{\sqrt{x} + 1} + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(2+(1+x**(1/2))**(1/2))**(1/2),x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(sqrt(sqrt(x) + 1) + 2),x, algorithm="giac")
[Out]