Optimal. Leaf size=31 \[ \frac{2 \left (\sqrt{x}-1\right )^{3/2} \left (\sqrt{x}+1\right )^{3/2}}{3 x^{3/2}} \]
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Rubi [A] time = 0.0353549, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.036 \[ \frac{2 \left (\sqrt{x}-1\right )^{3/2} \left (\sqrt{x}+1\right )^{3/2}}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 4.33842, size = 27, normalized size = 0.87 \[ \frac{2 \left (\sqrt{x} - 1\right )^{\frac{3}{2}} \left (\sqrt{x} + 1\right )^{\frac{3}{2}}}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-1+x**(1/2))**(1/2)*(1+x**(1/2))**(1/2)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0186333, size = 34, normalized size = 1.1 \[ \frac{2 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} (x-1)}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/x^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 23, normalized size = 0.7 \[{\frac{-2+2\,x}{3}\sqrt{-1+\sqrt{x}}\sqrt{1+\sqrt{x}}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.52182, size = 14, normalized size = 0.45 \[ \frac{2 \,{\left (x - 1\right )}^{\frac{3}{2}}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215258, size = 104, normalized size = 3.35 \[ -\frac{2 \,{\left (3 \,{\left (2 \, x - 1\right )} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 6 \, x^{2} + 6 \, x - 1\right )}}{3 \,{\left (4 \, x^{3} -{\left (4 \, x^{2} - x\right )} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 3 \, x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{\sqrt{x} - 1} \sqrt{\sqrt{x} + 1}}{x^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-1+x**(1/2))**(1/2)*(1+x**(1/2))**(1/2)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213755, size = 65, normalized size = 2.1 \[ \frac{16 \,{\left (3 \,{\left (\sqrt{\sqrt{x} + 1} - \sqrt{\sqrt{x} - 1}\right )}^{8} + 16\right )}}{3 \,{\left ({\left (\sqrt{\sqrt{x} + 1} - \sqrt{\sqrt{x} - 1}\right )}^{4} + 4\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1)/x^(5/2),x, algorithm="giac")
[Out]