Optimal. Leaf size=41 \[ \frac{10 x}{\sqrt{\sqrt{x^2+25}+5}}+\frac{2 x^3}{3 \left (\sqrt{x^2+25}+5\right )^{3/2}} \]
[Out]
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Rubi [A] time = 0.0199868, antiderivative size = 41, 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 \[ \frac{10 x}{\sqrt{\sqrt{x^2+25}+5}}+\frac{2 x^3}{3 \left (\sqrt{x^2+25}+5\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[5 + Sqrt[25 + x^2]],x]
[Out]
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Rubi in Sympy [A] time = 1.14524, size = 36, normalized size = 0.88 \[ \frac{2 x^{3}}{3 \left (\sqrt{x^{2} + 25} + 5\right )^{\frac{3}{2}}} + \frac{10 x}{\sqrt{\sqrt{x^{2} + 25} + 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5+(x**2+25)**(1/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0820932, size = 44, normalized size = 1.07 \[ \frac{2 \left (\sqrt{x^2+25}-5\right ) \sqrt{\sqrt{x^2+25}+5} \left (\sqrt{x^2+25}+10\right )}{3 x} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[5 + Sqrt[25 + x^2]],x]
[Out]
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Maple [C] time = 0.022, size = 64, normalized size = 1.6 \[ -{\frac{5\,\sqrt{5}}{8\,\sqrt{\pi }} \left ( -{\frac{32\,\sqrt{\pi }\sqrt{2}{x}^{3}}{375}\cosh \left ({\frac{3}{2}{\it Arcsinh} \left ({\frac{x}{5}} \right ) } \right ) }-8\,{\frac{\sqrt{\pi }\sqrt{2}\sinh \left ( 3/2\,{\it Arcsinh} \left ( x/5 \right ) \right ) }{\sqrt{1/25\,{x}^{2}+1}} \left ( -{\frac{4\,{x}^{4}}{1875}}-{\frac{2\,{x}^{2}}{75}}+2/3 \right ) } \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5+(x^2+25)^(1/2))^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{\sqrt{x^{2} + 25} + 5}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x^2 + 25) + 5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.287792, size = 41, normalized size = 1. \[ \frac{2 \,{\left (x^{2} + 5 \, \sqrt{x^{2} + 25} - 25\right )} \sqrt{\sqrt{x^{2} + 25} + 5}}{3 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x^2 + 25) + 5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.93124, size = 197, normalized size = 4.8 \[ - \frac{\sqrt{2} x^{3} \Gamma \left (- \frac{1}{4}\right ) \Gamma \left (\frac{1}{4}\right )}{12 \pi \sqrt{x^{2} + 25} \sqrt{\sqrt{x^{2} + 25} + 5} + 60 \pi \sqrt{\sqrt{x^{2} + 25} + 5}} - \frac{15 \sqrt{2} x \sqrt{x^{2} + 25} \Gamma \left (- \frac{1}{4}\right ) \Gamma \left (\frac{1}{4}\right )}{12 \pi \sqrt{x^{2} + 25} \sqrt{\sqrt{x^{2} + 25} + 5} + 60 \pi \sqrt{\sqrt{x^{2} + 25} + 5}} - \frac{75 \sqrt{2} x \Gamma \left (- \frac{1}{4}\right ) \Gamma \left (\frac{1}{4}\right )}{12 \pi \sqrt{x^{2} + 25} \sqrt{\sqrt{x^{2} + 25} + 5} + 60 \pi \sqrt{\sqrt{x^{2} + 25} + 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5+(x**2+25)**(1/2))**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{\sqrt{x^{2} + 25} + 5}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x^2 + 25) + 5),x, algorithm="giac")
[Out]