Optimal. Leaf size=11 \[ -\frac {2}{\sqrt {x}+1} \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {261} \[ -\frac {2}{\sqrt {x}+1} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {1}{\left (1+\sqrt {x}\right )^2 \sqrt {x}} \, dx &=-\frac {2}{1+\sqrt {x}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \[ -\frac {2}{\sqrt {x}+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.96, size = 12, normalized size = 1.09 \[ -\frac {2 \, {\left (\sqrt {x} - 1\right )}}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 9, normalized size = 0.82 \[ -\frac {2}{\sqrt {x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.91 \[ -\frac {2}{\sqrt {x}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 9, normalized size = 0.82 \[ -\frac {2}{\sqrt {x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.82 \[ -\frac {2}{\sqrt {x}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.36, size = 8, normalized size = 0.73 \[ - \frac {2}{\sqrt {x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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