Optimal. Leaf size=160 \[ \frac{8}{17} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{17/2}-\frac{56}{15} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{15/2}+\frac{144}{13} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{13/2}-\frac{160}{11} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{11/2}+8 \left (\sqrt{\sqrt{x-1}+1}+1\right )^{9/2}-\frac{24}{7} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{7/2}+\frac{16}{5} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{5/2} \]
[Out]
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Rubi [A] time = 0.427808, antiderivative size = 160, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ \frac{8}{17} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{17/2}-\frac{56}{15} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{15/2}+\frac{144}{13} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{13/2}-\frac{160}{11} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{11/2}+8 \left (\sqrt{\sqrt{x-1}+1}+1\right )^{9/2}-\frac{24}{7} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{7/2}+\frac{16}{5} \left (\sqrt{\sqrt{x-1}+1}+1\right )^{5/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + Sqrt[1 + Sqrt[-1 + x]]]*x,x]
[Out]
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Rubi in Sympy [A] time = 16.6857, size = 139, normalized size = 0.87 \[ \frac{8 \left (\sqrt{\sqrt{x - 1} + 1} + 1\right )^{\frac{17}{2}}}{17} - \frac{56 \left (\sqrt{\sqrt{x - 1} + 1} + 1\right )^{\frac{15}{2}}}{15} + \frac{144 \left (\sqrt{\sqrt{x - 1} + 1} + 1\right )^{\frac{13}{2}}}{13} - \frac{160 \left (\sqrt{\sqrt{x - 1} + 1} + 1\right )^{\frac{11}{2}}}{11} + 8 \left (\sqrt{\sqrt{x - 1} + 1} + 1\right )^{\frac{9}{2}} - \frac{24 \left (\sqrt{\sqrt{x - 1} + 1} + 1\right )^{\frac{7}{2}}}{7} + \frac{16 \left (\sqrt{\sqrt{x - 1} + 1} + 1\right )^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(1+(1+(-1+x)**(1/2))**(1/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.105612, size = 103, normalized size = 0.64 \[ \frac{8 \left (\sqrt{\sqrt{x-1}+1}+1\right )^{5/2} \left (8 \left (84 \sqrt{x-1} \sqrt{\sqrt{x-1}+1}-3030 \sqrt{\sqrt{x-1}+1}+1715 \sqrt{x-1}+2591\right )+77 \left (-377 \sqrt{\sqrt{x-1}+1}+195 \sqrt{x-1}+365\right ) x\right )}{255255} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 + Sqrt[1 + Sqrt[-1 + x]]]*x,x]
[Out]
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Maple [A] time = 0.012, size = 107, normalized size = 0.7 \[{\frac{16}{5} \left ( 1+\sqrt{1+\sqrt{-1+x}} \right ) ^{{\frac{5}{2}}}}-{\frac{24}{7} \left ( 1+\sqrt{1+\sqrt{-1+x}} \right ) ^{{\frac{7}{2}}}}+8\, \left ( 1+\sqrt{1+\sqrt{-1+x}} \right ) ^{9/2}-{\frac{160}{11} \left ( 1+\sqrt{1+\sqrt{-1+x}} \right ) ^{{\frac{11}{2}}}}+{\frac{144}{13} \left ( 1+\sqrt{1+\sqrt{-1+x}} \right ) ^{{\frac{13}{2}}}}-{\frac{56}{15} \left ( 1+\sqrt{1+\sqrt{-1+x}} \right ) ^{{\frac{15}{2}}}}+{\frac{8}{17} \left ( 1+\sqrt{1+\sqrt{-1+x}} \right ) ^{{\frac{17}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(1+(1+(-1+x)^(1/2))^(1/2))^(1/2),x)
[Out]
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Maxima [A] time = 0.727086, size = 143, normalized size = 0.89 \[ \frac{8}{17} \,{\left (\sqrt{\sqrt{x - 1} + 1} + 1\right )}^{\frac{17}{2}} - \frac{56}{15} \,{\left (\sqrt{\sqrt{x - 1} + 1} + 1\right )}^{\frac{15}{2}} + \frac{144}{13} \,{\left (\sqrt{\sqrt{x - 1} + 1} + 1\right )}^{\frac{13}{2}} - \frac{160}{11} \,{\left (\sqrt{\sqrt{x - 1} + 1} + 1\right )}^{\frac{11}{2}} + 8 \,{\left (\sqrt{\sqrt{x - 1} + 1} + 1\right )}^{\frac{9}{2}} - \frac{24}{7} \,{\left (\sqrt{\sqrt{x - 1} + 1} + 1\right )}^{\frac{7}{2}} + \frac{16}{5} \,{\left (\sqrt{\sqrt{x - 1} + 1} + 1\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*sqrt(sqrt(sqrt(x - 1) + 1) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.275021, size = 84, normalized size = 0.52 \[ \frac{8}{255255} \,{\left (15015 \, x^{2} +{\left (77 \, x + 1032\right )} \sqrt{x - 1} +{\left ({\left (1001 \, x + 4544\right )} \sqrt{x - 1} - 1176 \, x - 7696\right )} \sqrt{\sqrt{x - 1} + 1} - 1799 \, x - 22088\right )} \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*sqrt(sqrt(sqrt(x - 1) + 1) + 1),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(1+(1+(-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(x*sqrt(sqrt(sqrt(x - 1) + 1) + 1),x, algorithm="giac")
[Out]