Optimal. Leaf size=10 \[ 2 \log \left (\sqrt{x}+1\right ) \]
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Rubi [A] time = 0.0021274, antiderivative size = 10, 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 = {260} \[ 2 \log \left (\sqrt{x}+1\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{1}{\left (1+\sqrt{x}\right ) \sqrt{x}} \, dx &=2 \log \left (1+\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0012391, size = 10, normalized size = 1. \[ 2 \log \left (\sqrt{x}+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 9, normalized size = 0.9 \begin{align*} 2\,\ln \left ( \sqrt{x}+1 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.972923, size = 11, normalized size = 1.1 \begin{align*} 2 \, \log \left (\sqrt{x} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.20862, size = 27, normalized size = 2.7 \begin{align*} 2 \, \log \left (\sqrt{x} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.132629, size = 8, normalized size = 0.8 \begin{align*} 2 \log{\left (\sqrt{x} + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10207, size = 11, normalized size = 1.1 \begin{align*} 2 \, \log \left (\sqrt{x} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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