Optimal. Leaf size=15 \[ \frac {4}{3} \left (\sqrt {x}+1\right )^{3/2} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {261} \[ \frac {4}{3} \left (\sqrt {x}+1\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {\sqrt {1+\sqrt {x}}}{\sqrt {x}} \, dx &=\frac {4}{3} \left (1+\sqrt {x}\right )^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {4}{3} \left (\sqrt {x}+1\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 9, normalized size = 0.60 \[ \frac {4}{3} \, {\left (\sqrt {x} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 9, normalized size = 0.60 \[ \frac {4}{3} \, {\left (\sqrt {x} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.67 \[ \frac {4 \left (\sqrt {x}+1\right )^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 9, normalized size = 0.60 \[ \frac {4}{3} \, {\left (\sqrt {x} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.67, size = 9, normalized size = 0.60 \[ \frac {4\,{\left (\sqrt {x}+1\right )}^{3/2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.23, size = 31, normalized size = 2.07 \[ \frac {4 \sqrt {x} \sqrt {\sqrt {x} + 1}}{3} + \frac {4 \sqrt {\sqrt {x} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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