Optimal. Leaf size=12 \[ \frac{2}{3} \log \left (x^{3/2}+1\right ) \]
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Rubi [A] time = 0.0025368, antiderivative size = 12, 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} \[ \frac{2}{3} \log \left (x^{3/2}+1\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{\sqrt{x}}{1+x^{3/2}} \, dx &=\frac{2}{3} \log \left (1+x^{3/2}\right )\\ \end{align*}
Mathematica [A] time = 0.001608, size = 12, normalized size = 1. \[ \frac{2}{3} \log \left (x^{3/2}+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 9, normalized size = 0.8 \begin{align*}{\frac{2}{3}\ln \left ( 1+{x}^{{\frac{3}{2}}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.973684, size = 11, normalized size = 0.92 \begin{align*} \frac{2}{3} \, \log \left (x^{\frac{3}{2}} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.17086, size = 30, normalized size = 2.5 \begin{align*} \frac{2}{3} \, \log \left (x^{\frac{3}{2}} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.185694, size = 24, normalized size = 2. \begin{align*} \frac{2 \log{\left (\sqrt{x} + 1 \right )}}{3} + \frac{2 \log{\left (- \sqrt{x} + x + 1 \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11511, size = 27, normalized size = 2.25 \begin{align*} \frac{2}{3} \, \log \left (x - \sqrt{x} + 1\right ) + \frac{2}{3} \, \log \left (\sqrt{x} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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