Optimal. Leaf size=64 \[ \frac{8}{9} \left (\sqrt{\sqrt{x}+4}+2\right )^{9/2}-\frac{48}{7} \left (\sqrt{\sqrt{x}+4}+2\right )^{7/2}+\frac{64}{5} \left (\sqrt{\sqrt{x}+4}+2\right )^{5/2} \]
[Out]
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Rubi [A] time = 0.10365, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.235 \[ \frac{8}{9} \left (\sqrt{\sqrt{x}+4}+2\right )^{9/2}-\frac{48}{7} \left (\sqrt{\sqrt{x}+4}+2\right )^{7/2}+\frac{64}{5} \left (\sqrt{\sqrt{x}+4}+2\right )^{5/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[2 + Sqrt[4 + Sqrt[x]]],x]
[Out]
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Rubi in Sympy [A] time = 4.79705, size = 54, normalized size = 0.84 \[ \frac{8 \left (\sqrt{\sqrt{x} + 4} + 2\right )^{\frac{9}{2}}}{9} - \frac{48 \left (\sqrt{\sqrt{x} + 4} + 2\right )^{\frac{7}{2}}}{7} + \frac{64 \left (\sqrt{\sqrt{x} + 4} + 2\right )^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+(4+x**(1/2))**(1/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0395384, size = 62, normalized size = 0.97 \[ \frac{8}{315} \sqrt{\sqrt{\sqrt{x}+4}+2} \left (-64 \left (\sqrt{\sqrt{x}+4}+2\right )+35 x+2 \left (5 \sqrt{\sqrt{x}+4}+2\right ) \sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[2 + Sqrt[4 + Sqrt[x]]],x]
[Out]
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Maple [A] time = 0.014, size = 41, normalized size = 0.6 \[{\frac{64}{5} \left ( 2+\sqrt{4+\sqrt{x}} \right ) ^{{\frac{5}{2}}}}-{\frac{48}{7} \left ( 2+\sqrt{4+\sqrt{x}} \right ) ^{{\frac{7}{2}}}}+{\frac{8}{9} \left ( 2+\sqrt{4+\sqrt{x}} \right ) ^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+(4+x^(1/2))^(1/2))^(1/2),x)
[Out]
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Maxima [A] time = 0.733047, size = 54, normalized size = 0.84 \[ \frac{8}{9} \,{\left (\sqrt{\sqrt{x} + 4} + 2\right )}^{\frac{9}{2}} - \frac{48}{7} \,{\left (\sqrt{\sqrt{x} + 4} + 2\right )}^{\frac{7}{2}} + \frac{64}{5} \,{\left (\sqrt{\sqrt{x} + 4} + 2\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(sqrt(x) + 4) + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265884, size = 53, normalized size = 0.83 \[ \frac{8}{315} \,{\left (2 \,{\left (5 \, \sqrt{x} - 32\right )} \sqrt{\sqrt{x} + 4} + 35 \, x + 4 \, \sqrt{x} - 128\right )} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(sqrt(x) + 4) + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.12604, size = 216, normalized size = 3.38 \[ - \frac{2 \sqrt{2} \sqrt{x} \sqrt{\sqrt{x} + 4} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma \left (- \frac{1}{4}\right ) \Gamma \left (\frac{1}{4}\right )}{63 \pi } - \frac{4 \sqrt{2} \sqrt{x} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma \left (- \frac{1}{4}\right ) \Gamma \left (\frac{1}{4}\right )}{315 \pi } - \frac{\sqrt{2} x \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma \left (- \frac{1}{4}\right ) \Gamma \left (\frac{1}{4}\right )}{9 \pi } + \frac{64 \sqrt{2} \sqrt{\sqrt{x} + 4} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma \left (- \frac{1}{4}\right ) \Gamma \left (\frac{1}{4}\right )}{315 \pi } + \frac{128 \sqrt{2} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma \left (- \frac{1}{4}\right ) \Gamma \left (\frac{1}{4}\right )}{315 \pi } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+(4+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(sqrt(sqrt(sqrt(x) + 4) + 2),x, algorithm="giac")
[Out]