Optimal. Leaf size=26 \[ \frac {4 \left (\sqrt {\frac {1}{x}}+\frac {1}{x}\right )^{3/2}}{3 \left (\frac {1}{x}\right )^{3/2}} \]
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Rubi [A] time = 0.03, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {1966, 2014} \begin {gather*} \frac {4 \left (\sqrt {\frac {1}{x}}+\frac {1}{x}\right )^{3/2}}{3 \left (\frac {1}{x}\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 1966
Rule 2014
Rubi steps
\begin {align*} \int \sqrt {\sqrt {\frac {1}{x}}+\frac {1}{x}} \, dx &=-\operatorname {Subst}\left (\int \frac {\sqrt {\sqrt {x}+x}}{x^2} \, dx,x,\frac {1}{x}\right )\\ &=\frac {4 \left (\sqrt {\frac {1}{x}}+\frac {1}{x}\right )^{3/2}}{3 \left (\frac {1}{x}\right )^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 1.00 \begin {gather*} \frac {4 \left (\sqrt {\frac {1}{x}}+\frac {1}{x}\right )^{3/2}}{3 \left (\frac {1}{x}\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.07, size = 29, normalized size = 1.12 \begin {gather*} \frac {4}{3} \left (\sqrt {\frac {1}{x}}+1\right ) \sqrt {\sqrt {\frac {1}{x}}+\frac {1}{x}} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 18, normalized size = 0.69 \begin {gather*} \frac {4}{3} \, {\left (x + \sqrt {x}\right )} \sqrt {\frac {\sqrt {x} + 1}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 11, normalized size = 0.42 \begin {gather*} \frac {4}{3} \, {\left (\sqrt {x} + 1\right )}^{\frac {3}{2}} - \frac {4}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 32, normalized size = 1.23 \begin {gather*} \frac {4 \sqrt {\frac {\sqrt {\frac {1}{x}}\, x +1}{x}}\, \left (\sqrt {\frac {1}{x}}\, x +1\right )}{3 \sqrt {\frac {1}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {\frac {1}{\sqrt {x}} + \frac {1}{x}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \sqrt {\sqrt {\frac {1}{x}}+\frac {1}{x}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {\sqrt {\frac {1}{x}} + \frac {1}{x}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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