Optimal. Leaf size=11 \[ -\frac{2}{\sqrt{x}+1} \]
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Rubi [A] time = 0.0020008, antiderivative size = 11, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0017484, size = 11, normalized size = 1. \[ -\frac{2}{\sqrt{x}+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 0.9 \begin{align*} -2\, \left ( \sqrt{x}+1 \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.965887, size = 12, normalized size = 1.09 \begin{align*} -\frac{2}{\sqrt{x} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19421, size = 35, normalized size = 3.18 \begin{align*} -\frac{2 \,{\left (\sqrt{x} - 1\right )}}{x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.346045, size = 8, normalized size = 0.73 \begin{align*} - \frac{2}{\sqrt{x} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08511, size = 12, normalized size = 1.09 \begin{align*} -\frac{2}{\sqrt{x} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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